Computer architecture for emulating multi-dimensional string correlithm object dynamic time warping in a correlithm object processing system

ABSTRACT

A correlithm object processing system includes a memory that stores a sample two-dimensional data object represented by a horizontal string correlithm object and a vertical string correlithm object, and an example two-dimensional object represented by a horizontal string correlithm object and a vertical string correlithm object. The system determines a horizontal composite anti-Hamming distance by comparing the horizontal string correlithm objects to each other in n-dimensional space. The system determines a vertical composite anti-Hamming distance by comparing the vertical string correlithm objects to each other in n-dimensional space. The system sums the horizontal composite anti-Hamming distance with the vertical composite anti-Hamming distance to determine a composite anti-Hamming distance. The system determines the quality of a match between the example two-dimensional data object and the sample two-dimensional data object based on the composite anti-Hamming distance.

TECHNICAL FIELD

The present disclosure relates generally to computer architectures foremulating a processing system, and more specifically to a computerarchitecture for emulating multi-dimensional string correlithm objectdynamic time warping in a correlithm object processing system.

BACKGROUND

Conventional computers are highly attuned to using operations thatrequire manipulating ordinal numbers, especially ordinal binaryintegers. The value of an ordinal number corresponds with its positionin a set of sequentially ordered number values. These computers useordinal binary integers to represent, manipulate, and store information.These computers rely on the numerical order of ordinal binary integersrepresenting data to perform various operations such as counting,sorting, indexing, and mathematical calculations. Even when performingoperations that involve other number systems (e.g. floating point),conventional computers still resort to using ordinal binary integers toperform any operations.

Ordinal based number systems only provide information about the sequenceorder of the numbers themselves based on their numeric values. Ordinalnumbers do not provide any information about any other types ofrelationships for the data being represented by the numeric values suchas similarity. For example, when a conventional computer uses ordinalnumbers to represent data samples (e.g. images or audio signals),different data samples are represented by different numeric values. Thedifferent numeric values do not provide any information about howsimilar or dissimilar one data sample is from another. Unless there isan exact match in ordinal number values, conventional systems are unableto tell if a data sample matches or is similar to any other datasamples. As a result, conventional computers are unable to use ordinalnumbers by themselves for comparing different data samples and insteadthese computers rely on complex signal processing techniques.Determining whether a data sample matches or is similar to other datasamples is not a trivial task and poses several technical challenges forconventional computers. These technical challenges result in complexprocesses that consume processing power which reduces the speed andperformance of the system. The ability to compare unknown data samplesto known data samples is crucial for many security applications such asfacial recognition, voice recognition, and fraud detection.

Thus, it is desirable to provide a solution that allows computingsystems to efficiently determine how similar different data samples areto each other and to perform operations based on their similarity.

SUMMARY

Conventional computers are highly attuned to using operations thatrequire manipulating ordinal numbers, especially ordinal binaryintegers. The value of an ordinal number corresponds with its positionin a set of sequentially ordered number values. These computers useordinal binary integers to represent, manipulate, and store information.These computers rely on the numerical order of ordinal binary integersrepresenting data to perform various operations such as counting,sorting, indexing, and mathematical calculations. Even when performingoperations that involve other number systems (e.g. floating point),conventional computers still resort to using ordinal binary integers toperform any operations.

Ordinal based number systems only provide information about the sequenceorder of the numbers themselves based on their numeric values. Ordinalnumbers do not provide any information about any other types ofrelationships for the data being represented by the numeric values suchas similarity. For example, when a conventional computer uses ordinalnumbers to represent data samples (e.g. images or audio signals),different data samples are represented by different numeric values. Thedifferent numeric values do not provide any information about howsimilar or dissimilar one data sample is from another. Unless there isan exact match in ordinal number values, conventional systems are unableto tell if a data sample matches or is similar to any other datasamples. As a result, conventional computers are unable to use ordinalnumbers by themselves for comparing different data samples and insteadthese computers rely on complex signal processing techniques.Determining whether a data sample matches or is similar to other datasamples is not a trivial task and poses several technical challenges forconventional computers. These technical challenges result in complexprocesses that consume processing power which reduces the speed andperformance of the system. The ability to compare unknown data samplesto known data samples is crucial for many applications such as securityapplication (e.g. face recognition, voice recognition, and frauddetection).

The system described in the present application provides a technicalsolution that enables the system to efficiently determine how similardifferent objects are to each other and to perform operations based ontheir similarity. In contrast to conventional systems, the system usesan unconventional configuration to perform various operations usingcategorical numbers and geometric objects, also referred to ascorrelithm objects, instead of ordinal numbers. Using categoricalnumbers and correlithm objects on a conventional device involveschanging the traditional operation of the computer to supportrepresenting and manipulating concepts as correlithm objects. A deviceor system may be configured to implement or emulate a special purposecomputing device capable of performing operations using correlithmobjects. Implementing or emulating a correlithm object processing systemimproves the operation of a device by enabling the device to performnon-binary comparisons (i.e. match or no match) between different datasamples. This enables the device to quantify a degree of similaritybetween different data samples. This increases the flexibility of thedevice to work with data samples having different data types and/orformats, and also increases the speed and performance of the device whenperforming operations using data samples. These technical advantages andother improvements to the device are described in more detail throughoutthe disclosure.

In one embodiment, the system is configured to use binary integers ascategorical numbers rather than ordinal numbers which enables the systemto determine how similar a data sample is to other data samples.Categorical numbers provide information about similar or dissimilardifferent data samples are from each other. For example, categoricalnumbers can be used in facial recognition applications to representdifferent images of faces and/or features of the faces. The systemprovides a technical advantage by allowing the system to assigncorrelithm objects represented by categorical numbers to different datasamples based on how similar they are to other data samples. As anexample, the system is able to assign correlithm objects to differentimages of people such that the correlithm objects can be directly usedto determine how similar the people in the images are to each other. Inother words, the system can use correlithm objects in facial recognitionapplications to quickly determine whether a captured image of a personmatches any previously stored images without relying on conventionalsignal processing techniques. Correlithm object processing systems usenew types of data structures called correlithm objects that improve theway a device operates, for example, by enabling the device to performnon-binary data set comparisons and to quantify the similarity betweendifferent data samples. Correlithm objects are data structures designedto improve the way a device stores, retrieves, and compares data samplesin memory. Correlithm objects also provide a data structure that isindependent of the data type and format of the data samples theyrepresent. Correlithm objects allow data samples to be directly comparedregardless of their original data type and/or format.

A correlithm object processing system uses a combination of a sensortable, a node table, and/or an actor table to provide a specific set ofrules that improve computer-related technologies by enabling devices tocompare and to determine the degree of similarity between different datasamples regardless of the data type and/or format of the data samplethey represent. The ability to directly compare data samples havingdifferent data types and/or formatting is a new functionality thatcannot be performed using conventional computing systems and datastructures.

In addition, correlithm object processing system uses a combination of asensor table, a node table, and/or an actor table to provide aparticular manner for transforming data samples between ordinal numberrepresentations and correlithm objects in a correlithm object domain.Transforming data samples between ordinal number representations andcorrelithm objects involves fundamentally changing the data type of datasamples between an ordinal number system and a categorical number systemto achieve the previously described benefits of the correlithm objectprocessing system.

Using correlithm objects allows the system or device to compare datasamples (e.g. images) even when the input data sample does not exactlymatch any known or previously stored input values. For example, an inputdata sample that is an image may have different lighting conditions thanthe previously stored images. The differences in lighting conditions canmake images of the same person appear different from each other. Thedevice uses an unconventional configuration that implements a correlithmobject processing system that uses the distance between the data sampleswhich are represented as correlithm objects and other known data samplesto determine whether the input data sample matches or is similar to theother known data samples. Implementing a correlithm object processingsystem fundamentally changes the device and the traditional dataprocessing paradigm. Implementing the correlithm object processingsystem improves the operation of the device by enabling the device toperform non-binary comparisons of data samples. In other words, thedevice can determine how similar the data samples are to each other evenwhen the data samples are not exact matches. In addition, the device canquantify how similar data samples are to one another. The ability todetermine how similar data samples are to each other is unique anddistinct from conventional computers that can only perform binarycomparisons to identify exact matches.

A string correlithm object comprising a series of adjacent sub-stringcorrelithm objects whose cores overlap with each other to permit datavalues to be correlated with each other in n-dimensional space. Thedistance between adjacent sub-string correlithm objects can be selectedto create a tighter or looser correlation among the elements of thestring correlithm object in n-dimensional space. Thus, where data valueshave a pre-existing relationship with each other in the real-world,those relationships can be maintained in n-dimensional space if they arerepresented by sub-string correlithm objects of a string correlithmobject. In addition, new data values can be represented by sub-stringcorrelithm objects by interpolating the distance between those and otherdata values and representing that interpolation with sub-stringcorrelithm objects of a string correlithm object in n-dimensional space.The ability to migrate these relationships between data values in thereal world to relationships among correlithm objects provides asignificant advance in the ability to record, store, and faithfullyreproduce data within different computing environments. Furthermore, theuse of string correlithm objects significantly reduces the computationalburden of comparing time-varying sequences of data, or multi-dimensionaldata objects, with respect to conventional forms of executing dynamictime warping algorithms. The reduced computational burden results infaster processing speeds and reduced loads on memory structures used toperform the comparison of string correlithm objects.

The problems associated with comparing data sets and identifying matchesbased on the comparison are problems necessarily rooted in computertechnologies. As described above, conventional systems are limited to abinary comparison that can only determine whether an exact match isfound. Emulating a correlithm object processing system provides atechnical solution that addresses problems associated with comparingdata sets and identifying matches. Using correlithm objects to representdata samples fundamentally changes the operation of a device and how thedevice views data samples. By implementing a correlithm objectprocessing system, the device can determine the distance between thedata samples and other known data samples to determine whether the inputdata sample matches or is similar to the other known data samples. Inaddition, the device can determine a degree of similarity thatquantifies how similar different data samples are to one another.

Certain embodiments of the present disclosure may include some, all, ornone of these advantages. These advantages and other features will bemore clearly understood from the following detailed description taken inconjunction with the accompanying drawings and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of this disclosure, reference is nowmade to the following brief description, taken in connection with theaccompanying drawings and detailed description, wherein like referencenumerals represent like parts.

FIG. 1 is a schematic view of an embodiment of a special purposecomputer implementing correlithm objects in an n-dimensional space;

FIG. 2 is a perspective view of an embodiment of a mapping betweencorrelithm objects in different n-dimensional spaces;

FIG. 3 is a schematic view of an embodiment of a correlithm objectprocessing system;

FIG. 4 is a protocol diagram of an embodiment of a correlithm objectprocess flow;

FIG. 5 is a schematic diagram of an embodiment a computer architecturefor emulating a correlithm object processing system;

FIG. 6 illustrates an embodiment of how a string correlithm object maybe implemented within a node by a device;

FIG. 7 illustrates another embodiment of how a string correlithm objectmay be implemented within a node by a device;

FIG. 8 is a schematic diagram of another embodiment of a deviceimplementing string correlithm objects in a node for a correlithm objectprocessing system;

FIG. 9 is an embodiment of a graph of a probability distribution formatching a random correlithm object with a particular correlithm object;

FIG. 10 is a schematic diagram of an embodiment of a device implementinga correlithm object core in a node for a correlithm object processingsystem;

FIG. 11 is an embodiment of a graph of probability distributions foradjacent root correlithm objects;

FIG. 12A is an embodiment of a string correlithm object generator;

FIG. 12B is an embodiment of a table demonstrating a change in bitvalues associated with sub-string correlithm objects;

FIG. 13 is an embodiment of a process for generating a string correlithmobject;

FIG. 14 is an embodiment of discrete data values mapped to sub-stringcorrelithm objects of a string correlithm object;

FIG. 15A is an embodiment of analog data values mapped to sub-stringcorrelithm objects of a string correlithm object;

FIG. 15B is an embodiment of a table demonstrating how to map analogdata values to sub-string correlithm objects using interpolation;

FIG. 16 is an embodiment of non-string correlithm objects mapped tosub-string correlithm objects of a string correlithm object;

FIG. 17 is an embodiment of a process for mapping non-string correlithmobjects to sub-string correlithm objects of a string correlithm object;

FIG. 18 is an embodiment of sub-string correlithm objects of a firststring correlithm object mapped to sub-string correlithm objects of asecond string correlithm objects;

FIG. 19 is an embodiment of a process for mapping sub-string correlithmobjects of a first string correlithm object to sub-string correlithmobjects of a second string correlithm objects;

FIGS. 20A-C illustrate different embodiments of a distance table that isused to compare time-varying signals represented by string correlithmobjects in n-dimensional space; and

FIGS. 21A-D illustrate different embodiments of two-dimensional imagesthat are compared against each other using string correlithm objects.

DETAILED DESCRIPTION

FIGS. 1-5 describe various embodiments of how a correlithm objectprocessing system may be implemented or emulated in hardware, such as aspecial purpose computer. FIGS. 6-19 describe various embodiments of howa correlithm object processing system can generate and use stringcorrelithm objects to record and faithfully playback data values.

FIG. 1 is a schematic view of an embodiment of a user device 100implementing correlithm objects 104 in an n-dimensional space 102.Examples of user devices 100 include, but are not limited to, desktopcomputers, mobile phones, tablet computers, laptop computers, or otherspecial purpose computer platform. The user device 100 is configured toimplement or emulate a correlithm object processing system that usescategorical numbers to represent data samples as correlithm objects 104in a high-dimensional space 102, for example a high-dimensional binarycube. Additional information about the correlithm object processingsystem is described in FIG. 3. Additional information about configuringthe user device 100 to implement or emulate a correlithm objectprocessing system is described in FIG. 5.

Conventional computers rely on the numerical order of ordinal binaryintegers representing data to perform various operations such ascounting, sorting, indexing, and mathematical calculations. Even whenperforming operations that involve other number systems (e.g. floatingpoint), conventional computers still resort to using ordinal binaryintegers to perform any operations. Ordinal based number systems onlyprovide information about the sequence order of the numbers themselvesbased on their numeric values. Ordinal numbers do not provide anyinformation about any other types of relationships for the data beingrepresented by the numeric values, such as similarity. For example, whena conventional computer uses ordinal numbers to represent data samples(e.g. images or audio signals), different data samples are representedby different numeric values. The different numeric values do not provideany information about how similar or dissimilar one data sample is fromanother. In other words, conventional computers are only able to makebinary comparisons of data samples which only results in determiningwhether the data samples match or do not match. Unless there is an exactmatch in ordinal number values, conventional systems are unable to tellif a data sample matches or is similar to any other data samples. As aresult, conventional computers are unable to use ordinal numbers bythemselves for determining similarity between different data samples,and instead these computers rely on complex signal processingtechniques. Determining whether a data sample matches or is similar toother data samples is not a trivial task and poses several technicalchallenges for conventional computers. These technical challenges resultin complex processes that consume processing power which reduces thespeed and performance of the system.

In contrast to conventional systems, the user device 100 operates as aspecial purpose machine for implementing or emulating a correlithmobject processing system. Implementing or emulating a correlithm objectprocessing system improves the operation of the user device 100 byenabling the user device 100 to perform non-binary comparisons (i.e.match or no match) between different data samples. This enables the userdevice 100 to quantify a degree of similarity between different datasamples. This increases the flexibility of the user device 100 to workwith data samples having different data types and/or formats, and alsoincreases the speed and performance of the user device 100 whenperforming operations using data samples. These improvements and otherbenefits to the user device 100 are described in more detail below andthroughout the disclosure.

For example, the user device 100 employs the correlithm objectprocessing system to allow the user device 100 to compare data sampleseven when the input data sample does not exactly match any known orpreviously stored input values. Implementing a correlithm objectprocessing system fundamentally changes the user device 100 and thetraditional data processing paradigm. Implementing the correlithm objectprocessing system improves the operation of the user device 100 byenabling the user device 100 to perform non-binary comparisons of datasamples. In other words, the user device 100 is able to determine howsimilar the data samples are to each other even when the data samplesare not exact matches. In addition, the user device 100 is able toquantify how similar data samples are to one another. The ability todetermine how similar data samples are to each other is unique anddistinct from conventional computers that can only perform binarycomparisons to identify exact matches.

The user device's 100 ability to perform non-binary comparisons of datasamples also fundamentally changes traditional data searching paradigms.For example, conventional search engines rely on finding exact matchesor exact partial matches of search tokens to identify related datasamples. For instance, conventional text-based search engines arelimited to finding related data samples that have text that exactlymatches other data samples. These search engines only provide a binaryresult that identifies whether or not an exact match was found based onthe search token. Implementing the correlithm object processing systemimproves the operation of the user device 100 by enabling the userdevice 100 to identify related data samples based on how similar thesearch token is to other data sample. These improvements result inincreased flexibility and faster search time when using a correlithmobject processing system. The ability to identify similarities betweendata samples expands the capabilities of a search engine to include datasamples that may not have an exact match with a search token but arestill related and similar in some aspects. The user device 100 is alsoable to quantify how similar data samples are to each other based oncharacteristics besides exact matches to the search token. Implementingthe correlithm object processing system involves operating the userdevice 100 in an unconventional manner to achieve these technologicalimprovements as well as other benefits described below for the userdevice 100.

Computing devices typically rely on the ability to compare data sets(e.g. data samples) to one another for processing. For example, insecurity or authentication applications a computing device is configuredto compare an input of an unknown person to a data set of known people(or biometric information associated with these people). The problemsassociated with comparing data sets and identifying matches based on thecomparison are problems necessarily rooted in computer technologies. Asdescribed above, conventional systems are limited to a binary comparisonthat can only determine whether an exact match is found. As an example,an input data sample that is an image of a person may have differentlighting conditions than previously stored images. In this example,different lighting conditions can make images of the same person appeardifferent from each other. Conventional computers are unable todistinguish between two images of the same person with differentlighting conditions and two images of two different people withoutcomplicated signal processing. In both of these cases, conventionalcomputers can only determine that the images are different. This isbecause conventional computers rely on manipulating ordinal numbers forprocessing.

In contrast, the user device 100 uses an unconventional configurationthat uses correlithm objects to represent data samples. Using correlithmobjects to represent data samples fundamentally changes the operation ofthe user device 100 and how the device views data samples. Byimplementing a correlithm object processing system, the user device 100can determine the distance between the data samples and other known datasamples to determine whether the input data sample matches or is similarto the other known data samples, as explained in detail below. Unlikethe conventional computers described in the previous example, the userdevice 100 is able to distinguish between two images of the same personwith different lighting conditions and two images of two differentpeople by using correlithm objects 104. Correlithm objects allow theuser device 100 to determine whether there are any similarities betweendata samples, such as between two images that are different from eachother in some respects but similar in other respects. For example, theuser device 100 is able to determine that despite different lightingconditions, the same person is present in both images.

In addition, the user device 100 is able to determine a degree ofsimilarity that quantifies how similar different data samples are to oneanother. Implementing a correlithm object processing system in the userdevice 100 improves the operation of the user device 100 when comparingdata sets and identifying matches by allowing the user device 100 toperform non-binary comparisons between data sets and to quantify thesimilarity between different data samples. In addition, using acorrelithm object processing system results in increased flexibility andfaster search times when comparing data samples or data sets. Thus,implementing a correlithm object processing system in the user device100 provides a technical solution to a problem necessarily rooted incomputer technologies.

The ability to implement a correlithm object processing system providesa technical advantage by allowing the system to identify and comparedata samples regardless of whether an exact match has been previousobserved or stored. In other words, using the correlithm objectprocessing system the user device 100 is able to identify similar datasamples to an input data sample in the absence of an exact match. Thisfunctionality is unique and distinct from conventional computers thatcan only identify data samples with exact matches.

Examples of data samples include, but are not limited to, images, files,text, audio signals, biometric signals, electric signals, or any othersuitable type of data. A correlithm object 104 is a point in then-dimensional space 102, sometimes called an “n-space.” The value ofrepresents the number of dimensions of the space. For example, ann-dimensional space 102 may be a 3-dimensional space, a 50-dimensionalspace, a 100-dimensional space, or any other suitable dimension space.The number of dimensions depends on its ability to support certainstatistical tests, such as the distances between pairs of randomlychosen points in the space approximating a normal distribution. In someembodiments, increasing the number of dimensions in the n-dimensionalspace 102 modifies the statistical properties of the system to provideimproved results. Increasing the number of dimensions increases theprobability that a correlithm object 104 is similar to other adjacentcorrelithm objects 104. In other words, increasing the number ofdimensions increases the correlation between how close a pair ofcorrelithm objects 104 are to each other and how similar the correlithmobjects 104 are to each other.

Correlithm object processing systems use new types of data structurescalled correlithm objects 104 that improve the way a device operates,for example, by enabling the device to perform non-binary data setcomparisons and to quantify the similarity between different datasamples. Correlithm objects 104 are data structures designed to improvethe way a device stores, retrieves, and compares data samples in memory.Unlike conventional data structures, correlithm objects 104 are datastructures where objects can be expressed in a high-dimensional spacesuch that distance 106 between points in the space represent thesimilarity between different objects or data samples. In other words,the distance 106 between a pair of correlithm objects 104 in then-dimensional space 102 indicates how similar the correlithm objects 104are from each other and the data samples they represent. Correlithmobjects 104 that are close to each other are more similar to each otherthan correlithm objects 104 that are further apart from each other. Forexample, in a facial recognition application, correlithm objects 104used to represent images of different types of glasses may be relativelyclose to each other compared to correlithm objects 104 used to representimages of other features such as facial hair. An exact match between twodata samples occurs when their corresponding correlithm objects 104 arethe same or have no distance between them. When two data samples are notexact matches but are similar, the distance between their correlithmobjects 104 can be used to indicate their similarities. In other words,the distance 106 between correlithm objects 104 can be used to identifyboth data samples that exactly match each other as well as data samplesthat do not match but are similar. This feature is unique to acorrelithm processing system and is unlike conventional computers thatare unable to detect when data samples are different but similar in someaspects.

Correlithm objects 104 also provide a data structure that is independentof the data type and format of the data samples they represent.Correlithm objects 104 allow data samples to be directly comparedregardless of their original data type and/or format. In some instances,comparing data samples as correlithm objects 104 is computationally moreefficient and faster than comparing data samples in their originalformat. For example, comparing images using conventional data structuresinvolves significant amounts of image processing which is time consumingand consumes processing resources. Thus, using correlithm objects 104 torepresent data samples provides increased flexibility and improvedperformance compared to using other conventional data structures.

In one embodiment, correlithm objects 104 may be represented usingcategorical binary strings. The number of bits used to represent thecorrelithm object 104 corresponds with the number of dimensions of then-dimensional space 102 where the correlithm object 102 is located. Forexample, each correlithm object 104 may be uniquely identified using a64-bit string in a 64-dimensional space 102. As another example, eachcorrelithm object 104 may be uniquely identified using a 10-bit stringin a 10-dimensional space 102. In other examples, correlithm objects 104can be identified using any other suitable number of bits in a stringthat corresponds with the number of dimensions in the n-dimensionalspace 102.

In this configuration, the distance 106 between two correlithm objects104 can be determined based on the differences between the bits of thetwo correlithm objects 104. In other words, the distance 106 between twocorrelithm objects can be determined based on how many individual bitsdiffer between the correlithm objects 104. The distance 106 between twocorrelithm objects 104 can be computed using Hamming distance,anti-Hamming distance or any other suitable technique. As an exampleusing a 10-dimensional space 102, a first correlithm object 104 isrepresented by a first 10-bit string (1001011011) and a secondcorrelithm object 104 is represented by a second 10-bit string(1000011011). The Hamming distance corresponds with the number of bitsthat differ between the first correlithm object 104 and the secondcorrelithm object 104. Conversely, the anti-Hamming distance correspondswith the number of bits that are alike between the first correlithmobject 104 and the second correlithm object 104.Thus, the Hammingdistance between the first correlithm object 104 and the secondcorrelithm object 104 can be computed as follows:

$\quad\frac{\begin{matrix}1001011011 \\1000011011\end{matrix}}{0001000000}$

In this example, the Hamming distance is equal to one because only onebit differs between the first correlithm object 104 and the secondcorrelithm object. Conversely, the anti-Hamming distance is nine becausenine bits are the same between the first and second correlithm objects104. As another example, a third correlithm object 104 is represented bya third 10-bit string (0110100100). In this example, the Hammingdistance between the first correlithm object 104 and the thirdcorrelithm object 104 can be computed as follows:

$\quad\frac{\begin{matrix}1001011011 \\0110100100\end{matrix}}{1111111111}$

The Hamming distance is equal to ten because all of the bits aredifferent between the first correlithm object 104 and the thirdcorrelithm object 104. Conversely, the anti-Hamming distance is zerobecause none of the bits are the same between the first and thirdcorrelithm objects 104. In the previous example, a Hamming distanceequal to one indicates that the first correlithm object 104 and thesecond correlithm object 104 are close to each other in then-dimensional space 102, which means they are similar to each other.Similarly, an anti-Hamming distance equal to nine also indicates thatthe first and second correlithm objects are close to each other inn-dimensional space 102, which also means they are similar to eachother. In the second example, a Hamming distance equal to ten indicatesthat the first correlithm object 104 and the third correlithm object 104are further from each other in the n-dimensional space 102 and are lesssimilar to each other than the first correlithm object 104 and thesecond correlithm object 104. Similarly, an anti-Hamming distance equalto zero also indicates that that the first and third correlithm objects104 are further from each other in n-dimensional space 102 and are lesssimilar to each other than the first and second correlithm objects 104.In other words, the similarity between a pair of correlithm objects canbe readily determined based on the distance between the pair correlithmobjects, as represented by either Hamming distances or anti-Hammingdistances.

As another example, the distance between a pair of correlithm objects104 can be determined by performing an XOR operation between the pair ofcorrelithm objects 104 and counting the number of logical high values inthe binary string. The number of logical high values indicates thenumber of bits that are different between the pair of correlithm objects104 which also corresponds with the Hamming distance between the pair ofcorrelithm objects 104.

In another embodiment, the distance 106 between two correlithm objects104 can be determined using a Minkowski distance such as the Euclideanor “straight-line” distance between the correlithm objects 104. Forexample, the distance 106 between a pair of correlithm objects 104 maybe determined by calculating the square root of the sum of squares ofthe coordinate difference in each dimension.

The user device 100 is configured to implement or emulate a correlithmobject processing system that comprises one or more sensors 302, nodes304, and/or actors 306 in order to convert data samples between realworld values or representations and to correlithm objects 104 in acorrelithm object domain. Sensors 302 are generally configured toconvert real world data samples to the correlithm object domain. Nodes304 are generally configured to process or perform various operations oncorrelithm objects in the correlithm object domain. Actors 306 aregenerally configured to convert correlithm objects 104 into real worldvalues or representations. Additional information about sensors 302,nodes 304, and actors 306 is described in FIG. 3.

Performing operations using correlithm objects 104 in a correlithmobject domain allows the user device 100 to identify relationshipsbetween data samples that cannot be identified using conventional dataprocessing systems. For example, in the correlithm object domain, theuser device 100 is able to identify not only data samples that exactlymatch an input data sample, but also other data samples that havesimilar characteristics or features as the input data samples.Conventional computers are unable to identify these types ofrelationships readily. Using correlithm objects 104 improves theoperation of the user device 100 by enabling the user device 100 toefficiently process data samples and identify relationships between datasamples without relying on signal processing techniques that require asignificant amount of processing resources. These benefits allow theuser device 100 to operate more efficiently than conventional computersby reducing the amount of processing power and resources that are neededto perform various operations.

FIG. 2 is a schematic view of an embodiment of a mapping betweencorrelithm objects 104 in different n-dimensional spaces 102. Whenimplementing a correlithm object processing system, the user device 100performs operations within the correlithm object domain using correlithmobjects 104 in different n-dimensional spaces 102. As an example, theuser device 100 may convert different types of data samples having realworld values into correlithm objects 104 in different n-dimensionalspaces 102. For instance, the user device 100 may convert data samplesof text into a first set of correlithm objects 104 in a firstn-dimensional space 102 and data samples of audio samples as a secondset of correlithm objects 104 in a second n-dimensional space 102.Conventional systems require data samples to be of the same type and/orformat to perform any kind of operation on the data samples. In someinstances, some types of data samples cannot be compared because thereis no common format available. For example, conventional computers areunable to compare data samples of images and data samples of audiosamples because there is no common format. In contrast, the user device100 implementing a correlithm object processing system is able tocompare and perform operations using correlithm objects 104 in thecorrelithm object domain regardless of the type or format of theoriginal data samples.

In FIG. 2, a first set of correlithm objects 104A are defined within afirst n-dimensional space 102A and a second set of correlithm objects104B are defined within a second n-dimensional space 102B. Then-dimensional spaces may have the same number of dimensions or adifferent number of dimensions. For example, the first n-dimensionalspace 102A and the second n-dimensional space 102B may both be threedimensional spaces. As another example, the first n-dimensional space102A may be a three-dimensional space and the second n-dimensional space102B may be a nine dimensional space. Correlithm objects 104 in thefirst n-dimensional space 102A and second n-dimensional space 102B aremapped to each other. In other words, a correlithm object 104A in thefirst n-dimensional space 102A may reference or be linked with aparticular correlithm object 104B in the second n-dimensional space102B. The correlithm objects 104 may also be linked with and referencedwith other correlithm objects 104 in other n-dimensional spaces 102.

In one embodiment, a data structure such as table 200 may be used to mapor link correlithm objects 104 in different n-dimensional spaces 102. Insome instances, table 200 is referred to as a node table. Table 200 isgenerally configured to identify a first plurality of correlithm objects104 in a first n-dimensional space 102 and a second plurality ofcorrelithm objects 104 in a second n-dimensional space 102. Eachcorrelithm object 104 in the first n-dimensional space 102 is linkedwith a correlithm object 104 is the second n-dimensional space 102. Forexample, table 200 may be configured with a first column 202 that listscorrelithm objects 104A as source correlithm objects and a second column204 that lists corresponding correlithm objects 104B as targetcorrelithm objects. In other examples, table 200 may be configured inany other suitable manner or may be implemented using any other suitabledata structure. In some embodiments, one or more mapping functions maybe used to convert between a correlithm object 104 in a firstn-dimensional space and a correlithm object 104 is a secondn-dimensional space.

FIG. 3 is a schematic view of an embodiment of a correlithm objectprocessing system 300 that is implemented by a user device 100 toperform operations using correlithm objects 104. The system 300generally comprises a sensor 302, a node 304, and an actor 306. Thesystem 300 may be configured with any suitable number and/orconfiguration of sensors 302, nodes 304, and actors 306. An example ofthe system 300 in operation is described in FIG. 4. In one embodiment, asensor 302, a node 304, and an actor 306 may all be implemented on thesame device (e.g. user device 100). In other embodiments, a sensor 302,a node 304, and an actor 306 may each be implemented on differentdevices in signal communication with each other for example over anetwork. In other embodiments, different devices may be configured toimplement any combination of sensors 302, nodes 304, and actors 306.

Sensors 302 serve as interfaces that allow a user device 100 to convertreal world data samples into correlithm objects 104 that can be used inthe correlithm object domain. Sensors 302 enable the user device 100 tocompare and perform operations using correlithm objects 104 regardlessof the data type or format of the original data sample. Sensors 302 areconfigured to receive a real-world value 320 representing a data sampleas an input, to determine a correlithm object 104 based on the realworld value 320, and to output the correlithm object 104. For example,the sensor 302 may receive an image 301 of a person and output acorrelithm object 322 to the node 304 or actor 306. In one embodiment,sensors 302 are configured to use sensor tables 308 that link aplurality of real world values with a plurality of correlithm objects104 in an n-dimensional space 102. Real world values are any type ofsignal, value, or representation of data samples. Examples of real worldvalues include, but are not limited to, images, pixel values, text,audio signals, electrical signals, and biometric signals. As an example,a sensor table 308 may be configured with a first column 312 that listsreal world value entries corresponding with different images and asecond column 314 that lists corresponding correlithm objects 104 asinput correlithm objects. In other examples, sensor tables 308 may beconfigured in any other suitable manner or may be implemented using anyother suitable data structure. In some embodiments, one or more mappingfunctions may be used to translate between a real-world value 320 and acorrelithm object 104 in an n-dimensional space. Additional informationfor implementing or emulating a sensor 302 in hardware is described inFIG. 5.

Nodes 304 are configured to receive a correlithm object 104 (e.g. aninput correlithm object 104), to determine another correlithm object 104based on the received correlithm object 104, and to output theidentified correlithm object 104 (e.g.

an output correlithm object 104). In one embodiment, nodes 304 areconfigured to use node tables 200 that link a plurality of correlithmobjects 104 from a first n-dimensional space 102 with a plurality ofcorrelithm objects 104 in a second n-dimensional space 102. A node table200 may be configured similar to the table 200 described in FIG. 2.Additional information for implementing or emulating a node 304 inhardware is described in FIG. 5.

Actors 306 serve as interfaces that allow a user device 100 to convertcorrelithm objects 104 in the correlithm object domain back to realworld values or data samples. Actors 306 enable the user device 100 toconvert from correlithm objects 104 into any suitable type of real worldvalue. Actors 306 are configured to receive a correlithm object 104(e.g. an output correlithm object 104), to determine a real-world outputvalue 326 based on the received correlithm object 104, and to output thereal-world output value 326. The real-world output value 326 may be adifferent data type or representation of the original data sample. As anexample, the real-world input value 320 may be an image 301 of a personand the resulting real-world output value 326 may be text 327 and/or anaudio signal identifying the person. In one embodiment, actors 306 areconfigured to use actor tables 310 that link a plurality of correlithmobjects 104 in an n-dimensional space 102 with a plurality of real worldvalues. As an example, an actor table 310 may be configured with a firstcolumn 316 that lists correlithm objects 104 as output correlithmobjects and a second column 318 that lists real world values. In otherexamples, actor tables 310 may be configured in any other suitablemanner or may be implemented using any other suitable data structure. Insome embodiments, one or more mapping functions may be employed totranslate between a correlithm object 104 in an n-dimensional space anda real-world output value 326. Additional information for implementingor emulating an actor 306 in hardware is described in FIG. 5.

A correlithm object processing system 300 uses a combination of a sensortable 308, a node table 200, and/or an actor table 310 to provide aspecific set of rules that improve computer-related technologies byenabling devices to compare and to determine the degree of similaritybetween different data samples regardless of the data type and/or formatof the data sample they represent. The ability to directly compare datasamples having different data types and/or formatting is a newfunctionality that cannot be performed using conventional computingsystems and data structures. Conventional systems require data samplesto be of the same type and/or format in order to perform any kind ofoperation on the data samples. In some instances, some types of datasamples are incompatible with each other and cannot be compared becausethere is no common format available. For example, conventional computersare unable to compare data samples of images with data samples of audiosamples because there is no common format available. In contrast, adevice implementing a correlithm object processing system uses acombination of a sensor table 308, a node table 200, and/or an actortable 310 to compare and perform operations using correlithm objects 104in the correlithm object domain regardless of the type or format of theoriginal data samples. The correlithm object processing system 300 usesa combination of a sensor table 308, a node table 200, and/or an actortable 310 as a specific set of rules that provides a particular solutionto dealing with different types of data samples and allows devices toperform operations on different types of data samples using correlithmobjects 104 in the correlithm object domain. In some instances,comparing data samples as correlithm objects 104 is computationally moreefficient and faster than comparing data samples in their originalformat. Thus, using correlithm objects 104 to represent data samplesprovides increased flexibility and improved performance compared tousing other conventional data structures. The specific set of rules usedby the correlithm object processing system 300 go beyond simply usingroutine and conventional activities in order to achieve this newfunctionality and performance improvements.

In addition, correlithm object processing system 300 uses a combinationof a sensor table 308, a node table 200, and/or an actor table 310 toprovide a particular manner for transforming data samples betweenordinal number representations and correlithm objects 104 in acorrelithm object domain. For example, the correlithm object processingsystem 300 may be configured to transform a representation of a datasample into a correlithm object 104, to perform various operations usingthe correlithm object 104 in the correlithm object domain, and totransform a resulting correlithm object 104 into another representationof a data sample. Transforming data samples between ordinal numberrepresentations and correlithm objects 104 involves fundamentallychanging the data type of data samples between an ordinal number systemand a categorical number system to achieve the previously describedbenefits of the correlithm object processing system 300.

FIG. 4 is a protocol diagram of an embodiment of a correlithm objectprocess flow 400. A user device 100 implements process flow 400 toemulate a correlithm object processing system 300 to perform operationsusing correlithm object 104 such as facial recognition. The user device100 implements process flow 400 to compare different data samples (e.g.images, voice signals, or text) to each other and to identify otherobjects based on the comparison. Process flow 400 provides instructionsthat allows user devices 100 to achieve the improved technical benefitsof a correlithm object processing system 300.

Conventional systems are configured to use ordinal numbers foridentifying different data samples. Ordinal based number systems onlyprovide information about the sequence order of numbers based on theirnumeric values, and do not provide any information about any other typesof relationships for the data samples being represented by the numericvalues such as similarity. In contrast, a user device 100 can implementor emulate the correlithm object processing system 300 which provides anunconventional solution that uses categorical numbers and correlithmobjects 104 to represent data samples. For example, the system 300 maybe configured to use binary integers as categorical numbers to generatecorrelithm objects 104 which enables the user device 100 to performoperations directly based on similarities between different datasamples. Categorical numbers provide information about how similardifferent data sample are from each other. Correlithm objects 104generated using categorical numbers can be used directly by the system300 for determining how similar different data samples are from eachother without relying on exact matches, having a common data type orformat, or conventional signal processing techniques.

A non-limiting example is provided to illustrate how the user device 100implements process flow 400 to emulate a correlithm object processingsystem 300 to perform facial recognition on an image to determine theidentity of the person in the image. In other examples, the user device100 may implement process flow 400 to emulate a correlithm objectprocessing system 300 to perform voice recognition, text recognition, orany other operation that compares different objects.

At step 402, a sensor 302 receives an input signal representing a datasample. For example, the sensor 302 receives an image of person's faceas a real-world input value 320. The input signal may be in any suitabledata type or format. In one embodiment, the sensor 302 may obtain theinput signal in real-time from a peripheral device (e.g. a camera). Inanother embodiment, the sensor 302 may obtain the input signal from amemory or database.

At step 404, the sensor 302 identifies a real-world value entry in asensor table 308 based on the input signal. In one embodiment, thesystem 300 identifies a real-world value entry in the sensor table 308that matches the input signal. For example, the real-world value entriesmay comprise previously stored images. The sensor 302 may compare thereceived image to the previously stored images to identify a real-worldvalue entry that matches the received image. In one embodiment, when thesensor 302 does not find an exact match, the sensor 302 finds areal-world value entry that closest matches the received image.

At step 406, the sensor 302 identifies and fetches an input correlithmobject 104 in the sensor table 308 linked with the real-world valueentry. At step 408, the sensor 302 sends the identified input correlithmobject 104 to the node 304. In one embodiment, the identified inputcorrelithm object 104 is represented in the sensor table 308 using acategorical binary integer string. The sensor 302 sends the binarystring representing to the identified input correlithm object 104 to thenode 304.

At step 410, the node 304 receives the input correlithm object 104 anddetermines distances 106 between the input correlithm object 104 andeach source correlithm object 104 in a node table 200. In oneembodiment, the distance 106 between two correlithm objects 104 can bedetermined based on the differences between the bits of the twocorrelithm objects 104. In other words, the distance 106 between twocorrelithm objects can be determined based on how many individual bitsdiffer between a pair of correlithm objects 104. The distance 106between two correlithm objects 104 can be computed using Hammingdistance or any other suitable technique. In another embodiment, thedistance 106 between two correlithm objects 104 can be determined usinga Minkowski distance such as the Euclidean or “straight-line” distancebetween the correlithm objects 104. For example, the distance 106between a pair of correlithm objects 104 may be determined bycalculating the square root of the sum of squares of the coordinatedifference in each dimension.

At step 412, the node 304 identifies a source correlithm object 104 fromthe node table 200 with the shortest distance 106. A source correlithmobject 104 with the shortest distance from the input correlithm object104 is a correlithm object 104 either matches or most closely matchesthe received input correlithm object 104. At step 414, the node 304identifies and fetches a target correlithm object 104 in the node table200 linked with the source correlithm object 104. At step 416, the node304 outputs the identified target correlithm object 104 to the actor306. In this example, the identified target correlithm object 104 isrepresented in the node table 200 using a categorical binary integerstring. The node 304 sends the binary string representing to theidentified target correlithm object 104 to the actor 306.

At step 418, the actor 306 receives the target correlithm object 104 anddetermines distances between the target correlithm object 104 and eachoutput correlithm object 104 in an actor table 310. The actor 306 maycompute the distances between the target correlithm object 104 and eachoutput correlithm object 104 in an actor table 310 using a processsimilar to the process described in step 410.

At step 420, the actor 306 identifies an output correlithm object 104from the actor table 310 with the shortest distance 106. An outputcorrelithm object 104 with the shortest distance from the targetcorrelithm object 104 is a correlithm object 104 either matches or mostclosely matches the received target correlithm object 104. At step 422,the actor 306 identifies and fetches a real-world output value in theactor table 310 linked with the output correlithm object 104. Thereal-world output value may be any suitable type of data sample thatcorresponds with the original input signal. For example, the real-worldoutput value may be text that indicates the name of the person in theimage or some other identifier associated with the person in the image.As another example, the real-world output value may be an audio signalor sample of the name of the person in the image. In other examples, thereal-world output value may be any other suitable real world signal orvalue that corresponds with the original input signal. The real-worldoutput value may be in any suitable data type or format.

At step 424, the actor 306 outputs the identified real-world outputvalue. In one embodiment, the actor 306 may output the real-world outputvalue in real-time to a peripheral device (e.g. a display or a speaker).In one embodiment, the actor 306 may output the real-world output valueto a memory or database. In one embodiment, the real-world output valueis sent to another sensor 302. For example, the real-world output valuemay be sent to another sensor 302 as an input for another process.

FIG. 5 is a schematic diagram of an embodiment of a computerarchitecture 500 for emulating a correlithm object processing system 300in a user device 100. The computer architecture 500 comprises aprocessor 502, a memory 504, a network interface 506, and aninput-output (I/O) interface 508. The computer architecture 500 may beconfigured as shown or in any other suitable configuration.

The processor 502 comprises one or more processors operably coupled tothe memory 504. The processor 502 is any electronic circuitry including,but not limited to, state machines, one or more central processing unit(CPU) chips, logic units, cores (e.g. a multi-core processor),field-programmable gate array (FPGAs), application specific integratedcircuits (ASICs), graphics processing units (GPUs), or digital signalprocessors (DSPs). The processor 502 may be a programmable logic device,a microcontroller, a microprocessor, or any suitable combination of thepreceding. The processor 502 is communicatively coupled to and in signalcommunication with the memory 204. The one or more processors areconfigured to process data and may be implemented in hardware orsoftware. For example, the processor 502 may be 8-bit, 16-bit, 32-bit,64-bit or of any other suitable architecture. The processor 502 mayinclude an arithmetic logic unit (ALU) for performing arithmetic andlogic operations, processor registers that supply operands to the ALUand store the results of ALU operations, and a control unit that fetchesinstructions from memory and executes them by directing the coordinatedoperations of the ALU, registers and other components.

The one or more processors are configured to implement variousinstructions. For example, the one or more processors are configured toexecute instructions to implement sensor engines 510, node engines 512,actor engines 514, and string correlithm object engine 522. In anembodiment, the sensor engines 510, the node engines 512, the actorengines 514, and the string correlithm object engine 522 are implementedusing logic units, FPGAs, ASICs, DSPs, or any other suitable hardware.The sensor engines 510, the node engines 512, the actor engines 514, andthe string correlithm object engine 522 are each configured to implementa specific set of rules or processes that provides an improvedtechnological result.

In one embodiment, the sensor engine 510 is configured to receive areal-world value 320 as an input, to determine a correlithm object 104based on the real-world value 320, and to output the correlithm object104. An example of the sensor engine 510 in operation is described inFIG. 4.

In one embodiment, the node engine 512 is configured to receive acorrelithm object 104 (e.g. an input correlithm object 104), todetermine another correlithm object 104 based on the received correlithmobject 104, and to output the identified correlithm object 104 (e.g. anoutput correlithm object 104). The node engine 512 is also configured tocompute distances between pairs of correlithm objects 104. An example ofthe node engine 512 in operation is described in FIG. 4.

In one embodiment, the actor engine 514 is configured to receive acorrelithm object 104 (e.g. an output correlithm object 104), todetermine a real-world output value 326 based on the received correlithmobject 104, and to output the real-world output value 326. An example ofthe actor engine 514 in operation is described in FIG. 4.

In one embodiment, string correlithm object engine 522 is configured toimplement a string correlithm object generator 1200 and otherwiseprocess string correlithm objects 602, as described, for example, inFIGS. 12-19.

The memory 504 comprises one or more non-transitory disks, tape drives,or solid-state drives, and may be used as an over-flow data storagedevice, to store programs when such programs are selected for execution,and to store instructions and data that are read during programexecution. The memory 504 may be volatile or non-volatile and maycomprise read-only memory (ROM), random-access memory (RAM), ternarycontent-addressable memory (TCAM), dynamic random-access memory (DRAM),and static random-access memory (SRAM). The memory 504 is operable tostore sensor instructions 516, node instructions 518, actor instructions520, sensor tables 308, node tables 200, actor tables 310, stringcorrelithm object tables 1220, 1400, 1500, 1520, 1600, and 1820, and/orany other data or instructions. The sensor instructions 516, the nodeinstructions 518, and the actor instructions 520 comprise any suitableset of instructions, logic, rules, or code operable to execute thesensor engine 510, node engine 512, and the actor engine 514,respectively.

The sensor tables 308, the node tables 200, and the actor tables 310 maybe configured similar to the sensor tables 308, the node tables 200, andthe actor tables 310 described in FIG. 3, respectively.

The network interface 506 is configured to enable wired and/or wirelesscommunications. The network interface 506 is configured to communicatedata with any other device or system. For example, the network interface506 may be configured for communication with a modem, a switch, arouter, a bridge, a server, or a client. The processor 502 is configuredto send and receive data using the network interface 506.

The I/O interface 508 may comprise ports, transmitters, receivers,transceivers, or any other devices for transmitting and/or receivingdata with peripheral devices as would be appreciated by one of ordinaryskill in the art upon viewing this disclosure. For example, the I/Ointerface 508 may be configured to communicate data between theprocessor 502 and peripheral hardware such as a graphical userinterface, a display, a mouse, a keyboard, a key pad, and a touch sensor(e.g. a touch screen).

FIGS. 6 and 7 are schematic diagrams of an embodiment of a device 100implementing string correlithm objects 602 for a correlithm objectprocessing system 300. String correlithm objects 602 can be used by acorrelithm object processing system 300 to embed higher orders ofcorrelithm objects 104 within lower orders of correlithm objects 104.The order of a correlithm object 104 depends on the number of bits usedto represent the correlithm object 104. The order of a correlithm object104 also corresponds with the number of dimensions in the n-dimensionalspace 102 where the correlithm object 104 is located. For example, acorrelithm object 104 represented by a 64-bit string is a higher ordercorrelithm object 104 than a correlithm object 104 represented by 16-bitstring.

Conventional computing systems rely on accurate data input and areunable to detect or correct for data input errors in real time. Forexample, a conventional computing device assumes a data stream iscorrect even when the data stream has bit errors. When a bit erroroccurs that leads to an unknown data value, the conventional computingdevice is unable to resolve the error without manual intervention. Incontrast, string correlithm objects 602 enable a device 100 to performoperations such as error correction and interpolation within thecorrelithm object processing system 300. For example, higher ordercorrelithm objects 104 can be used to associate an input correlithmobject 104 with a lower order correlithm 104 when an input correlithmobject does not correspond with a particular correlithm object 104 in ann-dimensional space 102. The correlithm object processing system 300uses the embedded higher order correlithm objects 104 to definecorrelithm objects 104 between the lower order correlithm objects 104which allows the device 100 to identify a correlithm object 104 in thelower order correlithm objects n-dimensional space 102 that correspondswith the input correlithm object 104. Using string correlithm objects602, the correlithm object processing system 300 is able to interpolateand/or to compensate for errors (e.g. bit errors) which improve thefunctionality of the correlithm object processing system 300 and theoperation of the device 100.

In some instances, string correlithm objects 602 may be used torepresent a series of data samples or temporal data samples. Forexample, a string correlithm object 602 may be used to represent audioor video segments. In this example, media segments are represented bysequential correlithm objects that are linked together using a stringcorrelithm object 602.

FIG. 6 illustrates an embodiment of how a string correlithm object 602may be implemented within a node 304 by a device 100. In otherembodiments, string correlithm objects 602 may be integrated within asensor 302 or an actor 306. In 32-dimensional space 102 where correlithmobjects 104 can be represented by a 32-bit string, the 32-bit string canbe embedded and used to represent correlithm objects 104 in a lowerorder 3-dimensional space 102 which uses three bits. The 32-bit stringscan be partitioned into three 12-bit portions, where each portioncorresponds with one of the three bits in the 3-dimensional space 102.For example, the correlithm object 104 represented by the 3-bit binaryvalue of 000 may be represented by a 32-bit binary string of zeros andthe correlithm object represented by the binary value of 111 may berepresented by a 32- bit string of all ones. As another example, thecorrelithm object 104 represented by the 3-bit binary value of 100 maybe represented by a 32-bit binary string with 12 bits set to onefollowed by 24 bits set to zero. In other examples, string correlithmobjects 602 can be used to embed any other combination and/or number ofn-dimensional spaces 102.

In one embodiment, when a higher order n-dimensional space 102 isembedded in a lower order n-dimensional space 102, one or morecorrelithm objects 104 are present in both the lower order n-dimensionalspace 102 and the higher order n-dimensional space 102. Correlithmobjects 104 that are present in both the lower order n-dimensional space102 and the higher order n-dimensional space 102 may be referred to asparent correlithm objects 603. Correlithm objects 104 in the higherorder n-dimensional space 102 may be referred to as child correlithmobjects 604. In this example, the correlithm objects 104 in the3-dimensional space 102 may be referred to as parent correlithm objects603 while the correlithm objects 104 in the 32-dimensional space 102 maybe referred to as child correlithm objects 604. In general, childcorrelithm objects 604 are represented by a higher order binary stringthan parent correlithm objects 603. In other words, the bit strings usedto represent a child correlithm object 604 may have more bits than thebit strings used to represent a parent correlithm object 603. Thedistance between parent correlithm objects 603 may be referred to as astandard distance. The distance between child correlithm objects 604 andother child correlithm objects 604 or parent correlithm objects 603 maybe referred to as a fractional distance which is less than the standarddistance.

FIG. 7 illustrates another embodiment of how a string correlithm object602 may be implemented within a node 304 by a device 100. In otherembodiments, string correlithm objects 602 may be integrated within asensor 302 or an actor 306. In FIG. 7, a set of correlithm objects 104are shown within an n-dimensional space 102. In one embodiment, thecorrelithm objects 104 are equally spaced from adjacent correlithmobjects 104. A string correlithm object 602 comprises a parentcorrelithm object 603 linked with one or more child correlithm objects604. FIG. 7 illustrates three string correlithm objects 602 where eachstring correlithm object 602 comprises a parent correlithm object 603linked with six child correlithm objects 603. In other examples, then-dimensional space 102 may comprise any suitable number of correlithmobjects 104 and/or string correlithm objects 602.

A parent correlithm object 603 may be a member of one or more stringcorrelithm objects 602. For example, a parent correlithm object 603 maybe linked with one or more sets of child correlithm objects 604 in anode table 200. In one embodiment, a child correlithm object 604 mayonly be linked with one parent correlithm object 603. String correlithmobjects 602 may be configured to form a daisy chain or a linear chain ofchild correlithm objects 604. In one embodiment, string correlithmobjects 602 are configured such that child correlithm objects 604 do notform loops where the chain of child correlithm objects 604 intersectwith themselves. Each child correlithm objects 604 is less than thestandard distance away from its parent correlithm object 603. The childcorrelithm objects 604 are equally spaced from other adjacent childcorrelithm objects 604.

In one embodiment, a data structure such as node table 200 may be usedto map or link parent correlithm objects 603 with child correlithmobjects 604. The node table 200 is generally configured to identify aplurality of parent correlithm objects 603 and one or more childcorrelithm objects 604 linked with each of the parent correlithm objects603. For example, node table 200 may be configured with a first columnthat lists child correlithm objects 604 and a second column that listsparent correlithm objects 603. In other examples, the node table 200 maybe configured in any other suitable manner or may be implemented usingany other suitable data structure. In some embodiments, one or moremapping functions may be used to convert between a child correlithmobject 604 and a parent correlithm object 603.

FIG. 8 is a schematic diagram of another embodiment of a device 100implementing string correlithm objects 602 in a node 304 for acorrelithm object processing system 300. Previously in FIG. 7, a stringcorrelithm object 602 comprised of child correlithm objects 604 that areadjacent to a parent correlithm object 603. In FIG. 8, string correlithmobjects 602 comprise one or more child correlithm objects 604 in betweena pair of parent correlithm objects 603. In this configuration, thestring correlithm object 602 initially diverges from a first parentcorrelithm object 603A and then later converges toward a second parentcorrelithm object 603B. This configuration allows the correlithm objectprocessing system 300 to generate a string correlithm object 602 betweena particular pair of parent correlithm objects 603.

The string correlithm objects described in FIG. 8 allow the device 100to interpolate value between a specific pair of correlithm objects 104(i.e. parent correlithm objects 603). In other words, these types ofstring correlithm objects 602 allow the device 100 to performinterpolation between a set of parent correlithm objects 603.Interpolation between a set of parent correlithm objects 603 enables thedevice 100 to perform operations such as quantization which convertbetween different orders of correlithm objects 104.

In one embodiment, a data structure such as node table 200 may be usedto map or link the parent correlithm objects 603 with their respectivechild correlithm objects 604. For example, node table 200 may beconfigured with a first column that lists child correlithm objects 604and a second column that lists parent correlithm objects 603. In thisexample, a first portion of the child correlithm objects 604 is linkedwith the first parent correlithm object 603A and a second portion of thechild correlithm objects 604 is linked with the second parent correlithmobject 603B. In other examples, the node table 200 may be configured inany other suitable manner or may be implemented using any other suitabledata structure. In some embodiments, one or more mapping functions maybe used to convert between a child correlithm object 604 and a parentcorrelithm object 603.

FIG. 9 is an embodiment of a graph of a probability distribution 900 formatching a random correlithm object 104 with a particular correlithmobject 104. Axis 902 indicates the number of bits that are differentbetween a random correlithm object 104 with a particular correlithmobject 104. Axis 904 indicates the probability associated with aparticular number of bits being different between a random correlithmobject 104 and a particular correlithm object 104.

As an example, FIG. 9 illustrates the probability distribution 900 formatching correlithm objects 104 in a 64-dimensional space 102. In oneembodiment, the probability distribution 900 is approximately a Gaussiandistribution. As the number of dimensions in the n-dimensional space 102increases, the probability distribution 900 starts to shape more like animpulse response function. In other examples, the probabilitydistribution 900 may follow any other suitable type of distribution.

Location 906 illustrates an exact match between a random correlithmobject 104 with a particular correlithm object 104. As shown by theprobability distribution 900, the probability of an exact match betweena random correlithm object 104 with a particular correlithm object 104is extremely low. In other words, when an exact match occurs the eventis most likely deliberate and not a random occurrence.

Location 908 illustrates when all of the bits between the randomcorrelithm object 104 with the particular correlithm object 104 aredifferent. In this example, the random correlithm object 104 and theparticular correlithm object 104 have 64 bits that are different fromeach other. As shown by the probability distribution 900, theprobability of all the bits being different between the randomcorrelithm object 104 and the particular correlithm object 104 is alsoextremely low.

Location 910 illustrates an average number of bits that are differentbetween a random correlithm object 104 and the particular correlithmobject 104. In general, the average number of different bits between therandom correlithm object 104 and the particular correlithm object 104 isequal to

$\frac{n}{2}$

(also referred to as standard distance), where ‘n’ is the number ofdimensions in the n-dimensional space 102. In this example, the averagenumber of bits that are different between a random correlithm object 104and the particular correlithm object 104 is 32 bits.

Location 912 illustrates a cutoff region that defines a core distancefor a correlithm object core. The correlithm object 104 at location 906may also be referred to as a root correlithm object for a correlithmobject core. The core distance defines the maximum number of bits thatcan be different between a correlithm object 104 and the root correlithmobject to be considered within a correlithm object core for the rootcorrelithm object. In other words, the core distance defines the maximumnumber of hops away a correlithm object 104 can be from a rootcorrelithm object to be considered a part of the correlithm object corefor the root correlithm object. Additional information about acorrelithm object core is described in FIG. 10. In this example, thecutoff region defines a core distance equal to six standard deviationsaway from the average number of bits that are different between a randomcorrelithm object 104 and the particular correlithm object 104. Ingeneral, the standard deviation is equal to

$\sqrt{\frac{n}{4}},$

where ‘n’ is the number of dimensions in the n-dimensional space 102. Inthis example, the standard deviation of the 64-dimensional space 102 isequal to 4 bits. This means the cutoff region (location 912) is located24 bits away from location 910 which is 8 bits away from the rootcorrelithm object at location 906. In other words, the core distance isequal to 8 bits. This means that the cutoff region at location 912indicates that the core distance for a correlithm object core includescorrelithm objects 104 that have up to 8 bits different then the rootcorrelithm object or are up to 8 hops away from the root correlithmobject. In other examples, the cutoff region that defines the coredistance may be equal any other suitable value. For instance, the cutoffregion may be set to 2, 4, 8, 10, 12, or any other suitable number ofstandard deviations away from location 910.

FIG. 10 is a schematic diagram of an embodiment of a device 100implementing a correlithm object core 1002 in a node 304 for acorrelithm object processing system 300. In other embodiments,correlithm object cores 1002 may be integrated with a sensor 302 or anactor 306. Correlithm object cores 1002 can be used by a correlithmobject processing system 300 to classify or group correlithm objects 104and/or the data samples they represent. For example, a set of correlithmobjects 104 can be grouped together by linking them with a correlithmobject core 1402. The correlithm object core 1002 identifies the classor type associated with the set of correlithm objects 104.

In one embodiment, a correlithm object core 1002 comprises a rootcorrelithm object 1004 that is linked with a set of correlithm objects104. The set of correlithm objects 104 that are linked with the rootcorrelithm object 1004 are the correlithm objects 104 which are locatedwithin the core distance of the root correlithm object 1004. The set ofcorrelithm objects 104 are linked with only one root correlithm object1004. The core distance can be computed using a process similar to theprocess described in FIG. 9. For example, in a 64-dimensional space 102with a core distance defined at six sigma (i.e. six standarddeviations), the core distance is equal to 8-bits. This means thatcorrelithm objects 104 within up to eight hops away from the rootcorrelithm object 1004 are members of the correlithm object core 1002for the root correlithm object 1004.

In one embodiment, a data structure such as node table 200 may be usedto map or link root correlithm objects 1004 with sets of correlithmobjects 104. The node table 200 is generally configured to identify aplurality of root correlithm objects 1004 and correlithm objects 104linked with the root correlithm objects 1004. For example, node table200 may be configured with a first column that lists correlithm objectcores 1002, a second column that lists root correlithm objects 1004, anda third column that lists correlithm objects 104. In other examples, thenode table 200 may be configured in any other suitable manner or may beimplemented using any other suitable data structure. In someembodiments, one or more mapping functions may be used to convertbetween correlithm objects 104 and a root correlithm object 1004.

FIG. 11 is an embodiment of a graph of probability distributions 1100for adjacent root correlithm objects 1004. Axis 1102 indicates thedistance between the root correlithm objects 1004, for example, in unitsof bits. Axis 1104 indicates the probability associated with the numberof bits being different between a random correlithm object 104 and aroot correlithm object 1004.

As an example, FIG. 11 illustrates the probability distributions foradjacent root correlithm objects 1004 in a 1024-dimensional space 102.Location 1106 illustrates the location of a first root correlithm object1004 with respect to a second root correlithm object 1004. Location 1108illustrates the location of the second root correlithm object 1004. Eachroot correlithm object 1004 is located an average distance away fromeach other which is equal to

$\frac{n}{2},$

where ‘n’ is the number of dimensions in the n-dimensional space 102. Inthis example, the first root correlithm object 1004 and the second rootcorrelithm object 1004 are 512 bits or 32 standard deviations away fromeach other.

In this example, the cutoff region for each root correlithm object 1004is located at six standard deviations from locations 1106 and 1108. Inother examples, the cutoff region may be located at any other suitablelocation. For example, the cutoff region defining the core distance mayone, two, four, ten, or any other suitable number of standard deviationsaway from the average distance between correlithm objects 104 in then-dimensional space 102. Location 1110 illustrates a first cutoff regionthat defines a first core distance 1114 for the first root correlithmobject 1004. Location 1112 illustrates a second cutoff region thatdefines a second core distance 1116 for the second root correlithmobject 1004.

In this example, the core distances for the first root correlithm object1004 and the second root correlithm object 1004 do not overlap with eachother. This means that correlithm objects 104 within the correlithmobject core 1002 of one of the root correlithm objects 1004 are uniquelyassociated with the root correlithm object 1004 and there is noambiguity.

FIG. 12A illustrates one embodiment of a string correlithm objectgenerator 1200 configured to generate a string correlithm object 602 asoutput. String correlithm object generator 1200 is implemented by stringcorrelithm object engine 522 and comprises a first processing stage 1202a communicatively and logically coupled to a second processing stage1202 b. First processing stage 1202 receives an input 1204 and outputs afirst sub-string correlithm object 1206 a that comprises an n-bitdigital word wherein each bit has either a value of zero or one. In oneembodiment, first processing stage 1202 generates the values of each bitrandomly. Input 1204 comprises one or more parameters used to determinethe characteristics of the string correlithm object 602. For example,input 1204 may include a parameter for the number of dimensions, n, inthe n-dimensional space 102 (e.g., 64, 128, 256, etc.) in which togenerate the string correlithm object 602. Input 1204 may also include adistance parameter, δ, that indicates a particular number of bits of then-bit digital word (e.g., 4, 8, 16, etc.) that will be changed from onesub-string correlithm object 1206 to the next in the string correlithmobject 602. Second processing stage 1202 b receives the first sub-stringcorrelithm object 1206 a and, for each bit of the first sub-stringcorrelithm object 1206 a up to the particular number of bits identifiedin the distance parameter, δ, changes the value from a zero to a one orfrom a one to a zero to generate a second sub-string correlithm object1206 b. The bits of the first sub-string correlithm object 1206 a thatare changed in value for the second sub-string correlithm object 1206 bare selected randomly from the n-bit digital word. The other bits of then-bit digital word in second sub-string correlithm object 1206 b remainthe same values as the corresponding bits of the first sub-stringcorrelithm object 1206 a.

FIG. 12B illustrates a table 1220 that demonstrates the changes in bitvalues from a first sub-string correlithm object 1206 a to a secondsub-string correlithm object 1206 b. In this example, assume that n=64such that each sub-string correlithm object 1206 of the stringcorrelithm object 602 is a 64-bit digital word. As discussed previouslywith regard to FIG. 9, the standard deviation is equal to

$\sqrt{\frac{n}{4}},$

or four bits, for a 64-dimensional space 102. In one embodiment, thedistance parameter, δ, is selected to equal the standard deviation. Inthis embodiment, the distance parameter is also four bits which meansthat four bits will be changed from each sub-string correlithm object1206 to the next in the string correlithm object 602. In otherembodiments where it is desired to create a tighter correlation amongsub-string correlithm objects 1206, a distance parameter may be selectedto be less than the standard deviation (e.g., distance parameter ofthree bits or less where standard deviation is four bits). In stillother embodiments where it is desired to create a looser correlationamong sub-string correlithm objects 1206, a distance parameter may beselected to be more than the standard deviation (e.g., distanceparameter of five bits or more where standard deviation is four bits).Table 1220 illustrates the first sub-string correlithm object 1206 a inthe first column having four bit values that are changed, by secondprocessing stage 1202 b, from a zero to a one or from a one to a zero togenerate second sub-string correlithm object 1206 b in the secondcolumn. By changing four bit values, the core of the first sub-stringcorrelithm object 1206 a overlaps in 64-dimensional space with the coreof the second sub-string correlithm object 1206 b.

Referring back to FIG. 12A, the second processing stage 1202 b receivesfrom itself the second sub-string correlithm object 1206 b as feedback.For each bit of the second sub-string correlithm object 1206 b up to theparticular number of bits identified by the distance parameter, thesecond processing stage 1202 b changes the value from a zero to a one orfrom a one to a zero to generate a third sub-string correlithm object1206 c. The bits of the second sub-string correlithm object 1206 b thatare changed in value for the third sub-string correlithm object 1206 care selected randomly from the n-bit digital word. The other bits of then-bit digital word in third sub-string correlithm object 1206 c remainthe same values as the corresponding bits of the second sub-stringcorrelithm object 1206 b. Referring back to table 1220 illustrated inFIG. 12B, the second sub-string correlithm object 1206 b in the secondcolumn has four bit values that are changed, by second processing stage1202 b, from a zero to a one or from a one to a zero to generate thirdsub-string correlithm object 1206 c in the third column.

Referring back to FIG. 12A, the second processing stage 1202 bsuccessively outputs a subsequent sub-string correlithm object 1206 bychanging bit values of the immediately prior sub-string correlithmobject 1206 received as feedback, as described above. This processcontinues for a predetermined number of sub-string correlithm objects1206 in the string correlithm object 602. Together, the sub-stringcorrelithm objects 1206 form a string correlthim object 602 in which thefirst sub-string correlithm object 1206 a precedes and is adjacent tothe second sub-string correlithm object 1206 b, the second sub-stringcorrelithm object 1206 b precedes and is adjacent to the thirdsub-string correlithm object 1206 c, and so on. Each sub-stringcorrelithm object 1206 is separated from an adjacent sub-stringcorrelithm object 1206 in n-dimensional space 102 by a number of bitsrepresented by the distance parameter, δ.

FIG. 13 is a flowchart of an embodiment of a process 1300 for generatinga string correlithm object 602. At step 1302, a first sub-stringcorrelithm object 1206 a is generated, such as by a first processingstage 1202 a of a string correlithm object generator 1200. The firstsub-string correlithm object 1206 a comprises an n-bit digital word. Atstep 1304, a bit of the n-bit digital word of the sub-string correlithmobject 1206 is randomly selected, and is changed at step 1306 from azero to a one or from a one to a zero. Execution proceeds to step 1308where it is determined whether to change additional bits in the n-bitdigital word. In general, process 1300 will change a particular numberof bits up to the distance parameter, δ. In one embodiment, as describedabove with regard to FIGS. 12A-B, the distance parameter is four bits.If additional bits remain to be changed in the sub-string correlithmobject 1206, then execution returns to step 1304. If all of the bits upto the particular number of bits in the distance parameter have alreadybeen changed, as determined at step 1308, then execution proceeds tostep 1310 where the second sub-string correlithm object 1206 b isoutput. The other bits of the n-bit digital word in second sub-stringcorrelithm object 1206 b remain the same values as the correspondingbits of the first sub-string correlithm object 1206 a.

Execution proceeds to step 1312 where it is determined whether togenerate additional sub-string correlithm objects 1206 in the stringcorrelithm object 602. If so, execution returns back to step 1304 andthe remainder of the process occurs again to change particular bits upto the number of bits in the distance parameter, δ. Each subsequentsub-string correlithm object 1206 is separated from the immediatelypreceding sub-string correlithm object 1206 in n-dimensional space 102by a number of bits represented by the distance parameter, δ. If no moresub-string correlithm objects 1206 are to be generated in the stringcorrelithm object 602, as determined at step 1312, execution of process1300 terminates at steps 1314.

A string correlithm object 602 comprising a series of adjacentsub-string correlithm objects 1206 whose cores overlap with each otherpermits data values to be correlated with each other in n-dimensionalspace 102. Thus, where discrete data values have a pre-existingrelationship with each other in the real-world, those relationships canbe maintained in n-dimensional space 102 if they are represented bysub-string correlithm objects of a string correlithm object 602. Forexample, the letters of an alphabet have a relationship with each otherin the real world. In particular, the letter “A” precedes the letters“B” and “C” but is closer to the letter “B” than the letter “C”. Thus,if the letters of an alphabet are to be represented by a stringcorrelithm object 602, the relationship between letter “A” and theletters “B” and “C” should be maintained such that “A” precedes but iscloser to letter “B” than letter “C.” Similarly, the letter “B” isequidistant to both letters “A” and “C,” but the letter “B” issubsequent to the letter “A” and preceding the letter “C”. Thus, if theletters of an alphabet are to be represented by a string correlithmobject 602, the relationship between letter “B” and the letters “A” and“C” should be maintained such that the letter “B” is equidistant butsubsequent to letter “A” and preceding letter “C.” The ability tomigrate these relationships between data values in the real world torelationships among correlithm objects provides a significant advance inthe ability to record, store, and faithfully reproduce data withindifferent computing environments.

FIG. 14 illustrates how data values that have pre-existing relationshipswith each other can be mapped to sub-string correlithm objects 1206 of astring correlithm object 602 in n-dimensional space 102 by stringcorrelithm object engine 522 to maintain their relationships to eachother. Although the following description of FIG. 14 is illustrated withrespect to letters of an alphabet as representing data values that havepre-existing relationships to each each other, other data values canalso be mapped to string correlithm objects 602 using the techniquesdiscussed herein. In particular, FIG. 14 illustrates a node table 1400stored in memory 504 that includes a column for a subset of sub-stringcorrelithm objects 1206 of a string correlithm object 602. The firstsub-string correlithm object 1206 a is mapped to a discrete data value,such as the letter “A” of the alphabet. The second sub-string correlithmobject 1206 b is mapped to a discrete data value, such as the letter “B”of the alphabet, and so on with sub-string correlithm objects 1206 c and1206 d mapped to the letters “C” and “D”. As discussed above, theletters of the alphabet have a correlation with each other, including asequence, an ordering, and a distance from each other. Thesecorrelations among letters of the alphabet could not be maintained asrepresented in n-dimensional space if each letter was simply mapped to arandom correlithm object 104. Accordingly, to maintain thesecorrelations, the letters of the alphabet are mapped to sub-stringcorrelation objects 1206 of a string correlation object 602. This isbecause, as described above, the adjacent sub-string correlation objects1206 of a string correlation object 602 also have a sequence, anordering, and a distance from each other that can be maintained inn-dimensional space.

In particular, just like the letters “A,” “B,” “C,” and “D” have anordered sequence in the real world, the sub-string correlithm objects1206 a, 1206 b, 1206 c, and 1206 d have an ordered sequence and distancerelationships to each other in n-dimensional space. Similarly, just likethe letter “A” precedes but is closer to the letter “B” than the letter“C” in the real world, so too does the sub-string correlithm object 1206a precede but is closer to the sub-string correlithm object 1206 b thanthe sub-string correlithm object 1206 c in n-dimensional space.Similarly, just like the letter “B” is equidistant to but in between theletters “A” and “C” in the real world, so too is the sub-stringcorrelithm object 1206 b equidistant to but in between the sub-stringcorrelithm objects 1206 a and 1206 c in n-dimensional space. Althoughthe letters of the alphabet are used to provide an example of data inthe real world that has a sequence, an ordering, and a distancerelationship to each other, one of skill in the art will appreciate thatany data with those characteristics in the real world can be representedby sub-string correlithm objects 1206 to maintain those relationships inn-dimensional space.

Because the sub-string correlithm objects 1206 of a string correlithmobject 602 maintains the sequence, ordering, and/or distancerelationships between real world data in n-dimensional space, node 304can output the real-world data values (e.g., letters of the alphabet) inthe sequence in which they occurred. In one embodiment, the sub-stringcorrelithm objects 1206 can also be associated with timestamps, t₁₋₄, toaid with maintaining the relationship of the real-world data with asequence using the time at which they occurred. For example, sub-stringcorrelithm object 1206 a can be associated with a first timestamp, t₁;sub-string correlithm object 1206 b can be associated with a secondtimestamp, t₂; and so on. In one embodiment where the real-world datarepresents frames of a video signal that occur at different times of anordered sequence, maintaining a timestamp in the node table 1400 aidswith the faithful reproduction of the real-world data at the correcttime in the ordered sequence. In this way, the node table 1400 can actas a recorder by recording discrete data values for a time periodextending from at least the first timestamp, t₁ to a later timestamp,t_(n). Also in this way, the node 304 is also configured to reproduce orplayback the real-world data represented by the sub-string correlithmobjects 1206 in the node table 1400 for a period of time extending fromat least the first timestamp, t₁ to a later timestamp, t_(n). Theability to record real-world data, associate it to sub-string correlithmobjects 1206 in n-dimensional space while maintaining its order,sequence, and distance relationships, and subsequently faithfullyreproduce the real-world data as originally recorded provides asignificant technical advantage to computing systems.

The examples described above relate to representing discrete datavalues, such as letters of an alphabet, using sub-string correlithmobjects 1206 of a string correlithm object 602. However, sub-stringcorrelithm objects 1206 also provide the flexibility to representnon-discrete data values, or analog data values, using interpolationfrom the real world to n-dimensional space 102. FIG. 15A illustrates howanalog data values that have pre-existing relationships with each othercan be mapped to sub-string correlithm objects 1206 of a stringcorrelithm object 602 in n-dimensional space 102 by string correlithmobject engine 522 to maintain their relationships to each other. FIG.15A illustrates a node table 1500 stored in memory 504 that includes acolumn for each sub-string correlithm object 1206 of a string correlithmobject 602. The first sub-string correlithm object 1206 a is mapped toan analog data value, such as the number “1.0”. The second sub-stringcorrelithm object 1206 b is mapped to an analog data value, such as thenumber “2.0”, and so on with sub-string correlithm objects 1206 c and1206 d mapped to the numbers “3.0” and “4.0.” Just like the letters ofthe alphabet described above, these numbers have a correlation with eachother, including a sequence, an ordering, and a distance from eachother. One difference between representing discrete data values (e.g.,letters of an alphabet) and analog data values (e.g., numbers) usingsub-string correlithm objects 1206 is that new analog data values thatfall between pre-existing analog data values can be represented usingnew sub-string correlithm objects 1206 using interpolation, as describedin detail below.

If node 304 receives an input representing an analog data value of 1.5,for example, then string correlithm object engine 522 can determine anew sub-string correlithm object 1206 that maintains the relationshipbetween this input of 1.5 and the other numbers that are alreadyrepresented by sub-string correlithm objects 1206. In particular, nodetable 1500 illustrates that the analog data value 1.0 is represented bysub-string correlithm object 1206 a and analog data value 2.0 isrepresented by sub-string correlithm object 1206 b. Because the analogdata value 1.5 is between the data values of 1.0 and 2.0, then a newsub-string correlithm object 1206 would be created in n-dimensionalspace 102 between sub-string correlithm objects 1206 a and 1206 b. Thisis done by interpolating the distance in n-dimensional space 102 betweensub-string correlithm objects 1206 a and 1206 b that corresponds to thedistance between 1.0 and 2.0 where 1.5 resides and representing thatinterpolation using an appropriate n-bit digital word. In this example,the analog data value of 1.5 is halfway between the data values of 1.0and 2.0. Therefore, the sub-string correlithm object 1206 that isdetermined to represent the analog data value of 1.5 would be halfwaybetween the sub-string correlithm objects 1206 a and 1206 b inn-dimensional space 102. Generating a sub-string correlithm object 1206that is halfway between sub-string correlithm objects 1206 a and 1206 bin n-dimensional space 102 involves modifying bits of the n-bit digitalwords representing the sub-string correlithm objects 1206 a and 1206 b.This process is illustrated with respect to FIG. 15B.

FIG. 15B illustrates a table 1520 with a first column representing then-bit digital word of sub-string correlithm object 1206 a that is mappedin the node table 1500 to the data value 1.0; a second columnrepresenting the n-bit digital word of sub-string correlithm object 1206b that is mapped in the node table 1500 to the data value 2.0; and athird column representing the n-bit digital word of sub-stringcorrelithm object 1206 ab that is generated and associated with the datavalue 1.5. Table 1520 is stored in memory 504. As described above withregard to table 1220, the distance parameter, δ, between adjacentsub-string correlithm objects 1206 a and 1206 b was chosen, in oneembodiment, to be four bits. This means that for a 64-bit digital word,four bits have been changed from a zero to a one or from a one to a zeroin order to generate sub-string correlithm object 1206 b from sub-stringcorrelithm object 1206 a.

In order to generate sub-string correlithm object 1206 ab to representthe data value of 1.5, a particular subset of those four changed bitsbetween sub-string correlithm objects 1206 a and 1206 b should bemodified. Moreover, the actual bits that are changed should be selectedsuccessively from one end of the n-bit digital word or the other end ofthe n-bit digital word. Because the data value of 1.5 is exactly halfwaybetween the data values of 1.0 and 2.0, then it can be determined thatexactly half of the four bits that are different between sub-stringcorrelithm object 1206 a and sub-string correlithm object 1206 b shouldbe changed to generate sub-string correlithm object 1206 ab. In thisparticular example, therefore, starting from one end of the n-bitdigital word as indicated by arrow 1522, the first bit that was changedfrom a value of one in sub-string correlithm object 1206 a to a value ofzero in sub-string correlithm object 1206 b is changed back to a valueof one in sub-string correlithm object 1206 ab. Continuing from the sameend of the n-bit digital word as indicated by arrow 1522, the next bitthat was changed from a value of one in sub-string correlithm object1206 a to a value of zero in sub-string correlithm object 1206 b ischanged back to a value of one in sub-string correlithm object 1206 ab.The other two of the four bits that were changed from sub-stringcorrelithm object 1206 a to sub-string correlithm object 1206 b are notchanged back. Accordingly, two of the four bits that were differentbetween sub-string correlithm objects 1206 a and 1206 b are changed backto the bit values that were in sub-string correlithm object 1206 a inorder to generate sub-string correlithm object 1206 ab that is halfwaybetween sub-string correlithm objects 1206 a and 1206 b in n-dimensionalspace 102 just like data value 1.5 is halfway between data values 1.0and 2.0 in the real world.

Other input data values can also be interpolated and represented inn-dimensional space 102, as described above. For example, if the inputdata value received was 1.25, then it is determined to be one-quarter ofthe distance from the data value 1.0 and three-quarters of the distancefrom the data value 2.0. Accordingly, a sub-string correlithm object1206 ab can be generated by changing back three of the four bits thatdiffer between sub-string correlithm objects 1206 a and 1206 b. In thisregard, the sub-string correlithm object 1206 ab (which represents thedata value 1.25) will only differ by one bit from the sub-stringcorrelithm object 1206 a (which represents the data value 1.0) inn-dimensional space 102. Similarly, if the input data value received was1.75, then it is determined to be three-quarters of the distance fromthe data value 1.0 and one-quarter of the distance from the data value2.0. Accordingly, a sub-string correlithm object 1206 ab can begenerated by changing back one of the four bits that differ betweensub-string correlithm objects 1206 a and 1206 b. In this regard, thesub-string correlithm object 1206 ab (which represents the data value1.75) will differ by one bit from the sub-string correlithm object 1206b (which represents the data value 2.0) in n-dimensional space 102. Inthis way, the distance between data values in the real world can beinterpolated to the distance between sub-string correlithm objects 1206in n-dimensional space 102 in order to preserve the relationships amonganalog data values.

Although the example above was detailed with respect to changing bitvalues from the top end of the n-bit digital word represented by arrow1522, the bit values can also be successively changed from the bottomend of the n-bit digital word. The key is that of the bit values thatdiffer from sub-string correlithm object 1206 a to sub-string correlithmobject 1206 b, the bit values that are changed to generate sub-stringcorrelithm object 1206 ab should be taken consecutively as they areencountered whether from the top end of the n-bit digital word (asrepresented by arrow 1522) or from the bottom end of the n-bit digitalword. This ensures that sub-string correlithm object 1206 ab willactually be between sub-string correlithm objects 1206 a and 1206 brather than randomly drifting away from both of sub-string correlithmobjects 1206 a and 1206 b in n-dimensional space 102.

FIG. 16 illustrates how real-world data values can be aggregated andrepresented by correlithm objects 104 (also referred to as non-stringcorrelithm objects 104), which are then linked to correspondingsub-string correlithm objects 1206 of a string correlithm object 602 bystring correlithm object engine 522. As described above with regard toFIG. 12A, a string correlithm object generator 1200 generates sub-stringcorrelithm objects 1206 that are adjacent to each other in n-dimensionalspace 102 to form a string correlithm object 602. The sub-stringcorrelithm objects 1206 a-n embody an ordering, sequence, and distancerelationships to each other in n-dimensional space 102. As described indetail below, non-string correlithm objects 104 can be mapped tocorresponding sub-string correlithm objects 1206 and stored in a nodetable 1600 to provide an ordering or sequence among them inn-dimensional space 102. This allows node table 1600 to record, store,and faithfully reproduce or playback a sequence of events that arerepresented by non-string correlithm objects 104 a-n. In one embodiment,the sub-string correlithm objects 1206 and the non-string correlithmobjects 104 can both be represented by the same length of digital word,n, (e.g., 64 bit, 128 bit, 256 bit). In another embodiment, thesub-string correlithm objects 1206 can be represented by a digital wordof one length, n, and the non-string correlithm objects 104 can berepresented by a digital word of a different length, m.

In a particular embodiment, the non-string correlithm objects 104 a-ncan represent aggregated real-world data. For example, real-world datamay be generated related to the operation of an automated teller machine(ATM). In this example, the ATM machine may have a video camera and amicrophone to tape both the video and audio portions of the operation ofthe ATM by one or more customers in a vestibule of a bank facility ordrive-through. The ATM machine may also have a processor that conductsand stores information regarding any transactions between the ATM andthe customer associated with a particular account. The bank facility maysimultaneously record video, audio, and transactional aspects of theoperation of the ATM by the customer for security, audit, or otherpurposes. By aggregating the real-world data values into non-stringcorrelithm objects 104 and associating those non-string correlithmobjects 104 with sub-string correlithm objects 1206, as described ingreater detail below, the correlithm object processing system maymaintain the ordering, sequence, and other relationships between thereal-world data values in n-dimensional space 102 for subsequentreproduction or playback. Although the example above is detailed withrespect to three particular types of real-world data (i.e., video,audio, transactional data associated with a bank ATM) that areaggregated and represented by correlithm objects 104, it should beunderstood that any suitable number and combination of different typesof real-world data can be aggregated and represented in this example.

For a period of time from t₁ to t_(n), the ATM records video, audio, andtransactional real-world data. For example, the period of time mayrepresent an hour, a day, a week, a month, or other suitable time periodof recording. The real-world video data is represented by videocorrelithm objects 1602. The real-world audio data is represented byaudio correlithm objects 1604. The real-world transaction data isrepresented by transaction correlithm objects 1606. The correlithmobjects 1602, 1604, and 1606 can be aggregated to form non-stringcorrelithm objects 104. For example, at a first time, ti, the ATMgenerates: (a) real-world video data that is represented as a firstvideo correlithm object 1602 a; (b) real-world audio data that isrepresented by a first audio correlithm object 1604 a; and (c)real-world transaction data that is represented by a first transactioncorrelithm object 1606 a. Correlithm objects 1602 a, 1604 a, and 1606 acan be represented as a single non-string correlithm object 104 a whichis then associated with first sub-string correlithm object 1206 a in thenode table 1600. In one embodiment, the timestamp, t₁, can also becaptured in the non-string correlithm object 104 a. In this way, threedifferent types of real-world data are captured, represented by anon-string correlithm object 104 and then associated with a portion ofthe string correlithm object 602.

Continuing with the example, at a second time, t₂, the ATM generates:(a) real-world video data that is represented as a second videocorrelithm object 1602 b; (b) real-world audio data that is representedby a second audio correlithm object 1604 b; and (c) real-worldtransaction data that is represented by a second transaction correlithmobject 1606 b. The second time, t₂, can be a predetermined time orsuitable time interval after the first time, t₁, or it can be at a timesubsequent to the first time, t₁, where it is determined that one ormore of the video, audio, or transaction data has changed in anmeaningful way (e.g., video data indicates that a new customer enteredthe vestibule of the bank facility; another audible voice is detected orthe customer has made an audible request to the ATM; or the customer isattempting a different transaction or a different part of the sametransaction). Correlithm objects 1602 b, 1604 b, and 1606 b can berepresented as a single non-string correlithm object 104 b which is thenassociated with second sub-string correlithm object 1206 b in the nodetable 1600. In one embodiment, the timestamp, t₂, can also be capturedin the non-string correlithm object 104 b.

Continuing with the example, at a third time, t₃, the ATM generates: (a)real-world video data that is represented as a third video correlithmobject 1602 c; (b) real-world audio data that is represented by a thirdaudio correlithm object 1604 c; and (c) real-world transaction data thatis represented by a third transaction correlithm object 1606 c. Thethird time, t₃, can be a predetermined time or suitable time intervalafter the second time, t₂, or it can be at a time subsequent to thesecond time, t₂, where it is determined that one or more of the video,audio, or transaction data has changed again in a meaningful way, asdescribed above. Correlithm objects 1602 c, 1604 c, and 1606 c can berepresented as a single non-string correlithm object 104 c which is thenassociated with third sub-string correlithm object 1206 c in the nodetable 1600. In one embodiment, the timestamp, t₃, can also be capturedin the non-string correlithm object 104 c.

Concluding with the example, at an n-th time, t_(n), the ATM generates:(a) real-world video data that is represented as an n-th videocorrelithm object 1602 n; (b) real-world audio data that is representedby an n-th audio correlithm object 1604 n; and (c) real-worldtransaction data that is represented by an n-th transaction correlithmobject 1606 n. The third time, t_(n), can be a predetermined time orsuitable time interval after a previous time, t_(n-1), or it can be at atime subsequent to the previous time, t_(n-1), where it is determinedthat one or more of the video, audio, or transaction data has changedagain in a meaningful way, as described above. Correlithm objects 1602n, 1604 n, and 1606 n can be represented as a single non-stringcorrelithm object 104 n which is then associated with n-th sub-stringcorrelithm object 1206 n in the node table 1600. In one embodiment, thetimestamp, t_(n), can also be captured in the non-string correlithmobject 104 n.

As illustrated in FIG. 16, different types of real-world data (e.g.,video, audio, transactional) can be captured and represented bycorrelithm objects 1602, 1604, and 1606 at particular timestamps. Thosecorrelithm objects 1602, 1604, and 1606 can be aggregated intocorrelithm objects 104. In this way, the real-world data can be “fannedin” and represented by a common correlithm object 104. By capturingreal-world video, audio, and transaction data at different relevanttimestamps from t₁-t_(n), representing that data in correlithm objects104, and then associating those correlithm objects 104 with sub-stringcorrelithm objects 1206 of a string correlithm object 602, the nodetable 1600 described herein can store vast amounts of real-world data inn-dimensional space 102 for a period of time while preserving theordering, sequence, and relationships among real-world data events andcorresponding correlithm objects 104 so that they can be faithfullyreproduced or played back in the real-world, as desired. This provides asignificant savings in memory capacity.

FIG. 17 is a flowchart of an embodiment of a process 1700 for linkingnon-string correlithm objects 104 with sub-string correlithm objects1206. At step 1702, string correlithm object generator 1200 generates afirst sub-string correlithm object 1206 a. Execution proceeds to step1704 where correlithm objects 104 are used to represent different typesof real-world data at a first timestamp, t₁. For example, correlithmobject 1602 a represents real-world video data; correlithm object 1604 arepresents real-world audio data; and correlithm object 1606 arepresents real-world transaction data. At step 1706, each of correlithmobjects 1602 a, 1604 a, and 1606 a captured at the first timestamp, t₁,are aggregated and represented by a non-string correlithm object 104 a.Execution proceeds to step 1708, where non-string correlithm object 104a is linked to sub-string correlithm object 1206 a, and this associationis stored in node table 1600 at step 1710. At step 1712, it isdetermined whether real-world data at the next timestamp should becaptured. For example, if a predetermined time interval since the lasttimestamp has passed or if a meaningful change to the real-world datahas occurred since the last timestamp, then execution returns to steps1702-1710 where another sub-string correlithm object 1206 is generated(step 1702); correlithm objects representing real-world data is capturedat the next timestamp (step 1704); those correlithm objects areaggregated and represented in a non-string correlithm object 104 (step1706); that non-string correlithm object 104 is linked with a sub-stringcorrelithm object 1206 (step 1708); and this association is stored inthe node table 1600 (step 1710). If no further real-world data is to becaptured at the next timestamp, as determined at step 1712, thenexecution ends at step 1714.

FIG. 18 illustrates how sub-string correlithm objects 1206 a-e of afirst string correlithm object 602 a are linked to sub-string correlithmobjects 1206 x-z of a second string correlithm object 602 b by stringcorrelithm object engine 522. The first string correlithm object 602 aincludes sub-string correlithm objects 1206 a-e that are separated fromeach other by a first distance 1802 in n-dimensional space 102. Thesecond string correlithm object 602 b includes sub-string correlithmobjects 1206 x-z that are separated from each other by a second distance1804 in n-dimensional space 102. In one embodiment, the sub-stringcorrelithm objects 1206 a-e of the first string correlithm object 602 aand the sub-string correlithm objects 1206 x-z can both be representedby the same length of digital word, n, (e.g., 64-bit, 128-bit, 256-bit).In another embodiment, the sub-string correlithm objects 1206 a-e of thefirst string correlithm object 602 a can be represented by a digitalword of one length, n, and the sub-string correlithm objects 1206 x-z ofthe second string correlithm object 602 b can be represented by adigital word of a different length, m. Each sub-string correlithm object1206 a-e represents a particular data value, such as a particular typeof real-world data value. When a particular sub-string correlithm object1206 a-e of the first string correlithm object 602 is mapped to aparticular sub-string correlithm object 1206 x-z of the second stringcorrelithm object 602, as described below, then the data valueassociated with the sub-string correlithm object 1206 a-e of the firststring correlithm object 602 a becomes associated with the mappedsub-string correlithm object 1206 x-z of the second string correlithmobject 602 b.

Mapping data represented by sub-string correlithm objects 1206 a-e of afirst string correlithm object 602 a in a smaller n-dimensional space102 (e.g., 64-bit digital word) where the sub-string correlithm objects1206 a-e are more tightly correlated to sub-string correlithm objects1206 x-z of a second string correlithm object 602 b in a largern-dimensional space 102 (e.g., 256-bit digital word) where thesub-string correlithm objects 1206 x-y are more loosely correlated (orvice versa) can provide several technical advantages in a correlithmobject processing system. For example, such a mapping can be used tocompress data and thereby save memory resources. In another example,such a mapping can be used to spread out data and thereby createadditional space in n-dimensions for the interpolation of data. In yetanother example, such a mapping can be used to apply a transformationfunction to the data (e.g., linear transformation function or non-lineartransformation function) from the first string correlithm object 602 ato the second string correlithm object 602 b.

The mapping of a first string correlithm object 602 a to a secondcorrelithm object 602 b operates, as described below. First, a node 304receives a particular sub-string correlithm object 1206, such as 1206 billustrated in FIG. 18. To map this particular sub-string correlithmobject 1206 b to the second correlithm object 602 b, the node 304determines the proximity of it to corresponding sub-string correlithmobjects 1206 x and 1206 y in second string correlithm object 602 b(e.g., by determining the Hamming distance between 1206 b and 1206 x,and between 1206 b and 1206 y). In particular, node 304 determines afirst proximity 1806 in n-dimensional space between the sub-stringcorrelithm object 1206 b and sub-string correlithm object 1206 x; anddetermines a second proximity 1808 in n-dimensional space between thesub-string correlithm object 1206 b and sub-string correlithm object1206 y. As illustrated in FIG. 18, the first proximity 1806 is smallerthan the second proximity 1808. Therefore, sub-string correlithm object1206 b is closer in n-dimensional space 102 to sub-string correlithmobject 1206 x than to sub-string correlithm object 1206 y. Accordingly,node 304 maps sub-string correlithm object 1206 b of first stringcorrelithm object 602 a to sub-string correlithm object 1206 x of secondstring correlithm object 602 b and maps this association in node table1820 stored in memory 504.

The mapping of the first string correlithm object 602 a to a secondcorrelithm object 602 b continues in operation, as described below. Thenode 304 receives another particular sub-string correlithm object 1206,such as 1206 c illustrated in FIG. 18. To map this particular sub-stringcorrelithm object 1206 c to the second correlithm object 602 b, the node304 determines the proximity of it to corresponding sub-stringcorrelithm objects 1206 x and 1206 y in second string correlithm object602 b. In particular, node 304 determines a first proximity 1810 inn-dimensional space between the sub-string correlithm object 1206 c andsub-string correlithm object 1206 x; and determines a second proximity1812 in n-dimensional space between the sub-string correlithm object1206 c and sub-string correlithm object 1206 y. As illustrated in FIG.18, the second proximity 1812 is smaller than the second proximity 1810.Therefore, sub-string correlithm object 1206 c is closer inn-dimensional space 102 to sub-string correlithm object 1206 y than tosub-string correlithm object 1206 x. Accordingly, node 304 mapssub-string correlithm object 1206 c of first string correlithm object602 a to sub-string correlithm object 1206 y of second string correlithmobject 602 b and maps this association in node table 1820.

The sub-string correlithm objects 1206 a-e may be associated withtimestamps in order to capture a temporal relationship among them andwith the mapping to sub-string correlithm objects 1206 x-z. For example,sub-string correlithm object 1206 a may be associated with a firsttimestamp, second sub-string correlithm object 1206 b may be associatedwith a second timestamp later than the first timestamp, and so on.

FIG. 19 is a flowchart of an embodiment of a process 1900 for linking afirst string correlithm object 602 a with a second string correlithmobject 602 b. At step 1902, a first string correlithm object 602 a isreceived at node 304. The first correlithm object 602 a includes a firstplurality of sub-string correlithm objects 1206, such as 1206 a-eillustrated in FIG. 18. Each of these sub-string correlithm objects 1206a-e are separated from each other by a first distance 1802 inn-dimensional space 102. At step 1904, a second string correlithm object602 b is received at node 304. The second correlithm object 602 bincludes a second plurality of sub-string correlithm objects 1206, suchas 1206 x-z illustrated in FIG. 18. Each of these sub-string correlithmobjects 1206 x-z are separated from each other by a second distance 1804in n-dimensional space 102. At step 1906, node 304 receives a particularsub-string correlithm object 1206 of the first string correlithm object602 a. At step 1908, node 304 determines a first proximity inn-dimensional space 102, such as proximity 1806 illustrated in FIG. 18,to a corresponding sub-string correlithm object 1206 of secondcorrelithm object 602 b, such as sub-string correlithm object 1206 xillustrated in FIG. 18. At step 1910, node 304 determines a secondproximity in n-dimensional space 102, such as proximity 1808 illustratedin FIG. 18, to a corresponding sub-string correlithm object 1206 ofsecond correlithm object 602 b, such as sub-string correlithm object1206 y illustrated in FIG. 18.

At step 1912, node 304 selects the sub-string correlithm object 1206 ofsecond string correlithm object 602 b to which the particular sub-stringcorrelithm object 1206 received at step 1906 is closest in n-dimensionalspace based upon the first proximity determined at step 1908 and thesecond proximity determined at step 1910. For example, as illustrated inFIG. 18, sub-string correlithm object 1206 b is closer in n-dimensionalspace to sub-string correlithm object 1206 x than sub-string correlithmobject 1206 y based on first proximity 1806 being smaller than secondproximity 1808. Execution proceeds to step 1914 where node 304 maps theparticular sub-string correlithm object 1206 received at step 1906 tothe sub-string correlithm object 1206 of second string correlithm object602 b selected at step 1912. At step 1916, node 304 determines whetherthere are any additional sub-string correlithm objects 1206 of firststring correlithm object 602 a to map to the second string correlithmobject 602 b. If so, execution returns to perform steps 1906 through1914 with respect to a different particular sub-string correlithm object1206 of first string correlithm object 602 a. If not, executionterminates at step 1918.

Dynamic time warping (DTW) is a technique used to measure similaritybetween temporal sequences of data that may vary in speed. Dynamic timewarping can be applied to temporal sequences of video, audio, graphics,or any other form of data that can be turned into a linear sequence. Oneapplication for DTW is automatic speech recognition to cope withdifferent speaking speeds. For example, DTW can be used to find anoptimal match between two given time-varying sequences where thesequences are “warped” non-linearly in the time dimension to determine ameasure of their similarity independent of certain non-linear variationsin the time dimension. A technical problem associated with using dynamictime warping is the heavy computational burden required to process realworld data using DTW algorithms. Examples of the computational burdeninclude significant delays in processing speeds and large consumption ofmemory. A technologically improved system is needed to compare anddetermine matches between temporal sequences of data without thecomputational burden of conventional forms of processing using dynamictime warping algorithms. Using string correlithm objects 602 torepresent real world data significantly reduces the computational burdenwith comparing time-varying sequences of data, such as voice signals. Asdescribed in detail above with respect to FIGS. 14-19, real world datacan be mapped to string correlithm objects 602 and then compared to eachother in n-dimensional space 102 to find matches. This approachalleviates the significant computational burden associated with dynamictime warping algorithms. One reason for the reduction in computationalburden is because string correlithm objects 602 in n-dimensional space102 can represent vast amounts of real-world data such that the amountof memory used to store string correlithm objects 602 is orders ofmagnitude less than that which is required to store the correspondingreal-world data. Additionally, processors can compare string correlithmobjects 602 to each other in n-dimensional space 102 with fasterexecution and with less processing power than is required to compare thecorresponding real-world data.

FIG. 20A illustrates one embodiment of a distance table 2000 a stored inmemory 504 that is used to compare one time-varying signal representedby a first string correlithm object 602 aa in n-dimensional space (e.g.,64-bit, 128-bit, 256-bit, etc.), such as a first voice signal, withanother time-varying signal represented as a second string correlithmobject 602 bb in n-dimensional space (e.g., 64-bit, 128-bit, 256-bit,etc.), such as a second voice signal. Memory 504 also stores stringcorrelithm objects 602 aa and 602 bb. In one embodiment, the first voicesignal may be a template voice signal that is to be compared against aseries of sample voice signals stored in a database to find a match. Thetemplate voice signal may be a word or phrase uttered by a first personor entity that is being compared with a series of sample voice signalsuttered by the same or different person or entity in order to find amatch. Such a comparison and matching process may be useful in voice orspeech recognition systems, or in natural language processing systems.The first voice signal is mapped to string correlithm object 602 aausing one or more of the techniques described above, for example, withrespect to FIGS. 14-19. For example, the first voice signal includesdata values that are mapped to sub-string correlithm objects 1206 aa₁₋₉. In this embodiment, the second voice signal may be one of thesample voice signals to be compared against the first voice signal. Thesecond voice signal is mapped to string correlithm object 602 bb usingone or more of the techniques described above, for example, with respectto FIGS. 14-19. For example, the second voice signal includes datavalues that are mapped to sub-string correlithm objects 1206 bb ₁₋₉.

In operation, string correlithm object engine 522 of processor 502performs a comparison of string correlithm object 602 aa with stringcorrlithm object 602 bb in n-dimensional space 102, as described indetail below. In particular, engine 522 compares each sub-stringcorrelithm object 1206 aa ₁₋₉ pairwise against each sub-stringcorrelithm object 12066 bb ₁₋₉, and determines anti-Hamming distancesbased on this pairwise comparison. As described above with respect toFIG. 1, the anti-Hamming distance calculation can be used to determinethe similarity between sub-string correlithm objects 1206 of the firststring correlithm object 602 aa and the second string correlithm object602 bb. As described above with reference to FIG. 9, the average numberof different bits between a random correlithm object and a particularcorrelithm object is equal to

$\frac{n}{2}$

(also referred to as standard distance), where ‘n’ is the number ofdimensions in the n-dimensional space 102. The standard deviation isequal to

$\sqrt{\frac{n}{4}},$

where ‘n’ is the number of dimensions in the n-dimensional space 102.Thus, if a sub-string correlithm object 1206 aa of string correlithmobject 602 aa is statistically dissimilar to a corresponding sub-stringcorrelithm object 1206 bb of string correlithm object 602 bb, then theanti-Hamming distance is expected to be roughly equal to the standarddistance. Therefore, if the n-dimensional space 102 is 64-bits, then theanti-Hamming distance between two dissimilar correlithm objects isexpected to be roughly 32. If a sub-string correlithm object 12066 aa ofstring correlithm object 602 aa is statistically similar to acorresponding sub-string correlithm object 1206 bb of string correlithmobject 602 bb, then the anti-Hamming distance is expected to be roughlyequal to six standard deviations more than the standard distance.Therefore, if the n-dimensional space 102 is 64-bits, then theanti-Hamming distance between similar correlithm objects is expected tobe roughly 56 or more (i.e., 32 (standard distance)+24 (six standarddeviations)=56). In other embodiments, if the anti-Hamming distance isequal to four or five standard deviations beyond the standard distance,then the correlithm objects are determined to be statistically similar.

The use of six standard deviations away from the standard distance todetermine statistical similarity is also appropriate in a largern-dimensional space 102, such as an n-space of 256-bits. For example, in256-space, standard distance is 256/2, or 128. The standard deviation isthe square root of (256/4), or 8. So an exact match between twocorrelithm objects 602 in 256-space, represented by a Hamming distanceof 0 and an anti-Hamming distance of 256, is a statistical event that is128/8, or 16 standard deviations from the expected or standard distance.Similarly, a perfect “inverse match” between two correlithm objects 602in 256-space, represented by a Hamming distance of 256 and ananti-Hamming distance of 0, is also a statistical event that is(256−128)/8, or 16 standard deviations from the expected or standarddistance. Accordingly, as the n-dimensional space 102 grows larger, thenumber of standard deviations between the peak of the binomialdistribution and its end points also grows larger. However, in theseexamples of 256-space where an exact match lies 16 standard deviationsfrom the standard distance, statistical similarity may still be found 6standard deviations from the standard distance.

Engine 522 determines the anti-Hamming distances between sub-stringcorrelithm object 1206 aa ₁ of first string correlithm object 602 aa andeach of the sub-string correlithm objects 1206 bb ₁₋₉ of secondcorrelithm object 602 bb, and stores those values in a first column 2010of table 2000 a. Engine 522 determines the anti-Hamming distancesbetween sub-string correlithm object 1206 aa ₂ of first stringcorrelithm object 602 aa and each of the sub-string correlithm objects1206 bb ₁₋₉ of second correlithm object 602 bb, and stores those valuesin a second column 2012 of table 2000 a. Engine 522 repeats the pairwisedetermination of anti-Hamming distances between sub-string correlithmobjects 1206 aa ₃₋₉ of first string correlithm object 602 aa and each ofthe sub-string correlithm objects 1206 bb ₁₋₉ of second correlithmobject 602 bb, and stores those values in columns 2014-2026 of table2000 a, respectively.

The anti-Hamming distance values represented in the cells of table 2000a indicate which sub-string correlithm objects 1206 aa are statisticallysimilar or dissimilar to corresponding sub-string correlithm objects1206 bb. Cells of table 2000 a having an anti-Hamming distance value of64 in them, for example, indicate a similarity between sub-stringcorrelithm objects 1206 aa and 1206 bb. Cells of table 2000 a with a‘SD’ in them (for standard distance), for example, indicate adissimilarity between sub-string correlithm objects 1206 aa and 1206 bb.Although particular cells of table 2000 a have an anti-Hamming distancevalue of 64 in them, indicating a statistical similarity betweenparticular sub-string correlithm objects 1206 aa and 1206 bb, engine 522determines that there is no discernible pattern of similarity among anygroup of neighboring sub-string correlithm objects 1206 aa and 1206 bb.This indicates that while there may be some sporadic similaritiesbetween string correlithm object 602 aa and string correlithm object 602bb, no meaningful portions of them are statistically similar to eachother. Given that string correlithm object 602 aa represents a firstvoice signal and string correlithm object 602 bb represents a secondvoice signal in this embodiment, this means that no meaningful portionof those voice signals are statistically similar to each other. In otherwords, they are not a match. Although statistical similarity isrepresented in table 2000 a with an anti-Hamming distance value of 64 invarious cells to indicate a match among sub-string correlithm objects1206, it should be understood that a statistical similarity can bedetermined with an anti-Hamming distance that is anywhere from four tosix standard deviations greater than the standard distance.

FIG. 20B illustrates one embodiment of a distance table 2000 b stored inmemory 504 that is used to compare the first voice signal represented byfirst string correlithm object 602 aa in n-dimensional space (e.g.,64-bit, 128-bit, 256-bit, etc.), with another time-varying signalrepresented as a third string correlithm object 602 cc in n-dimensionalspace (e.g., 64-bit, 128-bit, 256-bit, etc.), such as a third voicesignal. In this embodiment, the third voice signal may be one of thesample voice signals to be compared against the first voice signal. Thethird voice signal is mapped to string correlithm object 602 cc usingone or more of the techniques described above, for example, with respectto FIGS. 14-19. For example, the third voice signal includes data valuesthat are mapped to sub-string correlithm objects 1206 cc ₁₋₉. Memory 504stores string correlithm object 602 cc.

In operation, string correlithm object engine 522 of processor 502performs a comparison of string correlithm object 602 aa with stringcorrlithm object 602 cc in n-dimensional space 102, as described indetail below. In particular, engine 522 compares each sub-stringcorrelithm object 1206 aa ₁₋₉ pairwise against each sub-stringcorrelithm object 12066 cc ₁₋₉.

Engine 522 determines the anti-Hamming distance between sub-stringcorrelithm object 1206 aa ₁ of first string correlithm object 602 aa andeach of the sub-string correlithm objects 1206 cc ₁₋₉ of thirdcorrelithm object 602 cc, and stores those values in a first column 2010of table 2000 b. Engine 522 determines the anti-Hamming distance betweensub-string correlithm object 1206 aa ₂ of first string correlithm object602 aa and each of the sub-string correlithm objects 1206 cc ₉ of thirdcorrelithm object 602 cc, and stores those values in a second column2012 of table 2000 b. Engine 522 repeats the pairwise determination ofanti-Hamming distances between sub-string correlithm objects 1206 aa ₃₋₉of first string correlithm object 602 aa and each of the sub-stringcorrelithm objects 1206 cc ₁₋₉ of third correlithm object 602 cc, andstores those values in columns 2014-2026 of table 2000 b, respectively.

The anti-Hamming distance values represented in the cells of table 2000b indicate which sub-string correlithm objects 1206 aa are statisticallysimilar or dissimilar to corresponding sub-string correlithm objects1206 cc. Although many cells of table 2000 b have an anti-Hammingdistance value of 64 in them, indicating statistical similarity betweenparticular sub-string correlithm objects 1206 aa and 1206 cc, engine 522determines that there also exists a discernible pattern of similarityamong a group of five neighboring sub-string correlithm objects 1206 aa₃₋₇ and 1206 cc ₃₋₇. This pattern is represented as a trace 2030 in FIG.20B. This trace 2030 indicates that at least a portion of stringcorrelithm object 602 aa is statistically similar to at least a portionof string correlithm object 602 cc. The trace 2030 is seen in table 2000b as extending from a lower left cell to an upper right cell, where eachcell in the trace 2030 has an anti-Hamming distance value of 64 in it.Although statistical similarity is represented in table 2000 b with ananti-Hamming distance value of 64 in various cells to indicate a matchamong sub-string correlithm objects 1206, it should be understood that astatistical similarity can be determined with an anti-Hamming distancethat is anywhere from four to six standard deviations greater than thestandard distance.

Given that string correlithm object 602 aa represents a first voicesignal and string correlithm object 602 cc represents a third voicesignal, this means that there is a relevant portion of those voicesignals that are statistically similar to each other. In other words,there is a match between at least a portion of these respective voicesignals. Trace 2030 therefore identifies the location of a match betweenstring correlithm objects 602 aa and 602 cc (i.e., match between 1206 aa₃₋₇ and 1206 cc ₃₋₇), as well as the quality of that match. Once engine522 locates a trace 2030 in table 2000 b, engine 522 sums together theanti-Hamming distance calculations for the cells in the trace 2030 todetermine a composite anti-Hamming distance calculation 2032. In thisexample, the composite anti-Hamming distance calculation 2032 is 320.

FIG. 20C illustrates one embodiment of a distance table 2000 c stored inmemory 504 that is used to compare the first voice signal represented byfirst string correlithm object 602 aa in n-dimensional space (e.g.,64-bit, 128-bit, 256-bit, etc.), with another time-varying signalrepresented as a fourth string correlithm object 602 dd in n-dimensionalspace (e.g., 64-bit, 128-bit, 256-bit, etc.), such as a fourth voicesignal. In this embodiment, the fourth voice signal may be one of thesample voice signals to be compared against the first voice signal. Thefourth voice signal is mapped to string correlithm object 602 dd usingone or more of the techniques described above, for example, with respectto FIGS. 14-19. For example, the fourth voice signal includes datavalues that are mapped to sub-string correlithm objects 1206 dd ₁₋₉.Memory 504 stores fourth string correlithm object 602 dd.

In operation, string correlithm object engine 522 of processor 502performs a comparison of string correlithm object 602 aa with stringcorrlithm object 602 dd in n-dimensional space 102, as described indetail below. In particular, engine 522 compares each sub-stringcorrelithm object 1206 aa ₁₋₉ pairwise against each sub-stringcorrelithm object 12066 dd ₁₋₉.

Engine 522 determines the anti-Hamming distance between sub-stringcorrelithm object 1206 aa ₁ of first string correlithm object 602 aa andeach of the sub-string correlithm objects 1206 dd ₁₋₉ of fourthcorrelithm object 602 dd, and stores those values in a first column 2010of table 2000 c. Engine 522 determines the anti-Hamming distance betweensub-string correlithm object 1206 aa ₂ of first string correlithm object602 aa and each of the sub-string correlithm objects 1206 dd ₁₋₉ offourth correlithm object 602 dd, and stores those values in a secondcolumn 2012 of table 2000 c. Engine 522 repeats the pairwisedetermination of anti-Hamming distances between sub-string correlithmobjects 1206 aa ₃₋₉ of first string correlithm object 602 aa and each ofthe sub-string correlithm objects 1206 dd ₁₋₉ of fourth correlithmobject 602 dd, and stores those values in columns 2014-2026 of table2000 c, respectively. The anti-Hamming distance values represented inthe cells of table 2000 c indicate which sub-string correlithm objects1206 aa are statistically similar or dissimilar to correspondingsub-string correlithm objects 1206 dd.

Although numerous cells of table 2000 c have an anti-Hamming distance of64 in them, indicating statistical similarity between particularsub-string correlithm objects 1206 aa and 1206 dd, engine 522 determinesthat there exists a pattern of similarity among a group of nineneighboring sub-string correlithm objects 1206 aa ₁₋₉ and 1206 cc ₁₋₉.This pattern is represented as a trace 2040 in table 2000 c. This trace2040 indicates that a portion of string correlithm object 602 aa isstatistically similar to a corresponding portion of string correlithmobject 602 dd. The trace 2040 is seen in table 2000 c as extending fromthe lowermost left cell to the uppermost right cell, where each cell inthe trace 2040 has an anti-Hamming distance value of 64 in it. Althoughstatistical similarity is represented in table 2000 c with ananti-Hamming distance value of 64 in various cells to indicate a matchamong sub-string correlithm objects 1206, it should be understood that astatistical similarity can be determined with an anti-Hamming distancethat is anywhere from four to six standard deviations greater than thestandard distance.

Given that string correlithm object 602 aa represents a first voicesignal and string correlithm object 602 dd represents a fourth voicesignal, this means that there is a significant portion of those voicesignals that are statistically similar to each other. In other words,there is a close match between the entirety of these respective voicesignals. Trace 2040 therefore identifies the location of a match betweenstring correlithm objects 602 aa and 602 dd (i.e., match between 1206 aa₁₋₉ and 1206 dd ₁₋₉), as well as the quality of that match. Once engine522 locates a trace 2040 in table 2000 c, engine 522 sums together theanti-Hamming distance calculations for the cells in the trace 2040 todetermine a composite anti-Hamming distance calculation 2042. In thisexample, the composite anti-Hamming distance calculation 2042 is 576.Upon locating trace 2030 in table 2000 b and trace 2040 in table 2000 c,but no trace in table 2000 a, engine 522 determines that each of stringcorrelithm objects 602 cc and 602 dd are closer matches to stringcorrelithm object 602 aa than string correlithm object 602 bb.Furthermore, engine 522 further determines which of string correlithmobjects 602 cc and 602 dd is the closest match to string correlithmobject 602 aa by determining which string correlithm object 602 cc or602 dd has the largest composite anti-Hamming distance calculation. Inthis example, because string correlithm object 602 dd has a largercomposite anti-Hamming distance calculation than string correlithmobject 602 cc (i.e., 576>320), engine 522 determines that stringcorrelithm object 602 dd is the closest match to string correlithmobject 602 aa. Based on this determination, engine 522 furtherdetermines that the fourth voice signal is the closest match to thefirst voice signal.

The principles described above with respect to FIGS. 20A-C can beextended from a single dimensional data object, such as a voice signal,to a multi-dimensional data object, such as a two-dimensionalphotograph. In a multi-dimensional implementation, engine 522 canimplement a facial recognition system by comparing the data comprising atwo-dimensional image of a face, as represented by string correlithmobjects 602 v and 602 h, with the data comprising sample two-dimensionalimages of faces, also as represented by string correlithm objects 602 vand 602 h.

FIG. 21A illustrates an embodiment of a two-dimensional image 2100comprising pixels represented by real-world data. In this embodiment,image 2100 is a picture of a woman. Engine 522 represents the real-worlddata of image 2100 as a horizontal string correlithm object 602 h ₁ anda vertical string correlithm object 602 v ₁ pursuant to the techniquesdescribed above with respect to FIGS. 14-19. In particular, engine 522represents vertical slices of the real-world data in image 2100 (asrepresented by arrow 2102) in corresponding sub-string correlithmobjects 1206 v ₁₁₋₁₉. For example, engine 522 represents a firstvertical slice of the real-world data in image 2100 in sub-stringcorrelithm object 1206 v ₁₁; a second vertical slice of the real-worlddata in image 2100 in sub-string correlithm object 1206 v ₁₂; and so onfrom sub-string correlithm object 1206 v ₁₃ through sub-stringcorrelithm object 1206 v ₁₉. Similarly, engine 522 represents horizontalslices of the real-world data in image 2100 (as represented by arrow2104) in corresponding sub-string correlithm objects 1206 h ₁₁₋₁₉. Forexample, engine 522 represents a first horizontal slice of thereal-world data in image 2100 in sub-string correlithm object 1206 h ₁₁;a second vertical slice of the real-world data in image 2100 insub-string correlithm object 1206 h ₁₂; and so on from sub-stringcorrelithm object 1206 h ₁₃ through sub-string correlithm object 1206 h₁₉. Memory 504 stores string correlithm objects 602 v ₁ and 602 h ₁.

FIGS. 21B-D illustrate embodiments of two-dimensional images to becompared against image 2100 to determine similarities or a match. Inparticular, FIG. 21B illustrates an embodiment of a two-dimensionalimage 2110 comprising pixels represented by real-world data. In thisembodiment, image 2110 is a picture of a man. Engine 522 represents thereal-world data of image 2110 as a horizontal string correlithm object602 h ₂ and a vertical string correlithm object 602 v ₂ pursuant to thetechniques described above with respect to FIGS. 14-19. In particular,engine 522 represents vertical slices of the real-world data in image2110 (as represented by arrow 2112) in corresponding sub-stringcorrelithm objects 1206 v ₂₁₋₂₉. For example, engine 522 represents afirst vertical slice of the real-world data in image 2110 in sub-stringcorrelithm object 1206 v ₂₁; a second vertical slice of the real-worlddata in image 2110 in sub-string correlithm object 1206 v ₂₂; and so onfrom sub-string correlithm object 1206 v ₂₃ through sub-stringcorrelithm object 1206 v ₂₉. Similarly, engine 522 represents horizontalslices of the real-world data in image 2110 (as represented by arrow2114) in corresponding sub-string correlithm objects 1206 h ₂₁₋₂₉. Forexample, engine 522 represents a first horizontal slice of thereal-world data in image 2110 in sub-string correlithm object 1206 h ₂₁;a second vertical slice of the real-world data in image 2110 insub-string correlithm object 1206 h ₂₂; and so on from sub-stringcorrelithm object 1206 h ₂₃ through sub-string correlithm object 1206 h₂₉. Memory 504 stores string correlithm objects 602 v ₂ and 602 h ₂.

FIG. 21C illustrates an embodiment of a two-dimensional image 2120comprising pixels represented by real-world data. In this embodiment,image 2120 is a picture of a woman wearing glasses. Engine 522represents the real-world data of image 2120 as a horizontal stringcorrelithm object 602 h ₃ and a vertical string correlithm object 602 v₃ pursuant to the techniques described above with respect to FIGS.14-19. In particular, engine 522 represents vertical slices of thereal-world data in image 2120 (as represented by arrow 2122) incorresponding sub-string correlithm objects 1206 v ₃₁₋₃₉. For example,engine 522 represents a first vertical slice of the real-world data inimage 2120 in sub-string correlithm object 1206 v ₃₁; a second verticalslice of the real-world data in image 2120 in sub-string correlithmobject 1206 v ₃₂; and so on from sub-string correlithm object 1206 v ₃₃through sub-string correlithm object 1206 v ₃₉. Similarly, engine 522represents horizontal slices of the real-world data in image 2120 (asrepresented by arrow 2124) in corresponding sub-string correlithmobjects 1206 h ₃₁₋₃₉. For example, engine 522 represents a firsthorizontal slice of the real-world data in image 2120 in sub-stringcorrelithm object 1206 h ₃₁; a second vertical slice of the real-worlddata in image 2120 in sub-string correlithm object 1206 h ₃₂; and so onfrom sub-string correlithm object 1206 h ₃₃ through sub-stringcorrelithm object 1206 h ₃₉. Memory 504 stores string correlithm objects602 v ₃ and 602 h ₃.

FIG. 21D illustrates an embodiment of a two-dimensional image 2130comprising pixels represented by real-world data. In this embodiment,image 2130 is a picture of a young man. Engine 522 represents thereal-world data of image 2130 as a horizontal string correlithm object602 h ₄ and a vertical string correlithm object 602 v ₄ pursuant to thetechniques described above with respect to FIGS. 14-19. In particular,engine 522 represents vertical slices of the real-world data in image2130 (as represented by arrow 2132) in corresponding sub-stringcorrelithm objects 1206 v ₄₁₋₄₉. For example, engine 522 represents afirst vertical slice of the real-world data in image 2130 in sub-stringcorrelithm object 1206 v ₄₁; a second vertical slice of the real-worlddata in image 2130 in sub-string correlithm object 1206 v ₄₂; and so onfrom sub-string correlithm object 1206 v ₄₃ through sub-stringcorrelithm object 1206 v ₄₉. Similarly, engine 522 represents horizontalslices of the real-world data in image 2130 (as represented by arrow2134) in corresponding sub-string correlithm objects 1206 h ₄₁₋₄₉. Forexample, engine 522 represents a first horizontal slice of thereal-world data in image 2130 in sub-string correlithm object 1206 h ₄₁;a second vertical slice of the real-world data in image 2130 insub-string correlithm object 1206 h ₄₂; and so on from sub-stringcorrelithm object 1206 h ₄₃ through sub-string correlithm object 1206 h₄₉. Memory 504 stores string correlithm objects 602 v ₄ and 602 h ₄.

In operation, engine 522 compares each of the images 2110, 2120, and2130 against image 2100 in n-dimensional space 102 to determine the bestmatch. It does so by performing a comparison of string correlithm object602 v ₁ with each of string correlithm objects 602 v ₂₋₄ inn-dimensional space 102; and by performing a comparison of stringcorrelithm objects 602 h ₁ with each of string correlithm objects 602 h₂₋₄ in n-dimensional space 102. Engine 522 performs each of thehorizontal and vertical comparisons in n-dimensional space 102 bycalculating the anti-Hamming distances between corresponding pairs ofsub-string correlithm objects 1206, using the methodology describedabove with respect to FIGS. 20A-B. The following description of thisoperation is not described with respect to specific distance tables toavoid confusion, but it should be understood that the operationdescribed below uses distance tables to store the anti-Hamming distancevalues calculated by engine 522 when performing a pairwise comparison ofsub-string correlithm objects 1206, as described above with respect toFIGS. 20A-C.

Comparison of Image 2100 with Image 2110 in n-Dimensional Space

To compare image 2110 against image 2100 in n-dimensional space 102,engine 522 compares each sub-string correlithm object 1206 v ₁₁₋₁₉pairwise against each sub-string correlithm object 1206 v ₂₁₋₂₉ todetermine a plurality of anti-Hamming distances and stores them in afirst distance table, as described above with regard to FIGS. 20A-B.Engine 522 determines whether there is any discernible pattern ofsimilarity in the first distance table among any group of neighboringsub-string correlithm objects 1206 v ₁₁₋₁₉ and 1206 v ₂₁₋₂₉, asrepresented by the calculated anti-Hamming distances, as described abovewith regard to FIGS. 20A-B. If such a pattern of similarity is found(e.g., a trace), then engine 522 calculates a vertical compositeanti-Hamming distance 2116 by summing the anti-Hamming distance valueswithin the pattern.

Engine 522 also compares each sub-string correlithm object 1206 h ₁₁₋₁₉pairwise against each sub-string correlithm object 1206 h ₂₁₋₂₉ todetermine a plurality of anti-Hamming distances and stores them in asecond distance table, as described above with regard to FIGS. 20A-B.Engine 522 determines whether there is any discernible pattern ofsimilarity in the second distance table among any group of neighboringsub-string correlithm objects 1206 h ₁₁₋₁₉ and 1206 h ₂₁₋₂₉, asrepresented by the calculated anti-Hamming distances, as described abovewith regard to FIGS. 20A-B. If such a pattern of similarity is found(e.g., a trace), then engine 522 calculates a horizontal compositeanti-Hamming distance 2118 by summing the anti-Hamming distance valueswithin the pattern.

Engine 522 determines a composite anti-Hamming distance 2119 by summingthe vertical composite anti-Hamming distance 2116 and the horizontalcomposite anti-Hamming distance 2118. Engine 522 determines whether theimage 2110 is statistically similar to, or a match of, image 2100 basedon the magnitude of the calculated composite anti-Hamming distance 2119in comparison to a threshold. For example, in one embodiment, acomposite anti-Hamming distance 2119 that is roughly four standarddeviations greater than a standard distance composite value for then-dimensional string correlithm object 602 is considered to bestatistically similar.

Comparison of Image 2100 with Image 2120 in n-Dimensional Space

To compare image 2120 against image 2100 in n-dimensional space 102,engine 522 compares each sub-string correlithm object 1206 v ₁₁₋₁₉pairwise against each sub-string correlithm object 1206 v ₃₁₋₃₉ todetermine a plurality of anti-Hamming distances and stores them in afirst distance table, as described above with regard to FIGS. 20A-B.Engine 522 determines whether there is any discernible pattern ofsimilarity in the first distance table among any group of neighboringsub-string correlithm objects 1206 v ₁₁₋₁₉ and 1206 v ₃₁₋₃₉, asrepresented by the calculated anti-Hamming distances, as described abovewith regard to FIGS. 20A-B. If such a pattern of similarity is found(e.g., a trace), then engine 522 calculates a vertical compositeanti-Hamming distance 2126 by summing the anti-Hamming distance valueswithin the pattern.

Engine 522 also compares each sub-string correlithm object 1206 h ₁₁₋₁₉pairwise against each sub-string correlithm object 1206 h ₃₁₋₃₉ todetermine a plurality of anti-Hamming distances and stores them in asecond distance table, as described above with regard to FIGS. 20A-B.Engine 522 determines whether there is any discernible pattern ofsimilarity in the second distance table among any group of neighboringsub-string correlithm objects 1206 h ₁₁₋₁₉ and 1206 h ₃₁₋₃₉, asrepresented by the calculated anti-Hamming distances, as described abovewith regard to FIGS. 20A-B. If such a pattern of similarity is found(e.g., a trace), then engine 522 calculates a horizontal compositeanti-Hamming distance 2128 by summing the anti-Hamming distance valueswithin the pattern.

Engine 522 determines a composite anti-Hamming distance 2129 by summingthe vertical composite anti-Hamming distance 2126 and the horizontalcomposite anti-Hamming distance 2128. Engine 522 determines whether theimage 2120 is statistically similar to, or a match of, image 2100 basedon the magnitude of the calculated composite anti-Hamming distance 2129in comparison to a threshold. For example, in one embodiment, acomposite anti-Hamming distance 2129 that is roughly four standarddeviations greater than a standard distance composite value for then-dimensional string correlithm object 602 is considered to bestatistically similar.

Comparison of Image 2100 with Image 2130 in n-Dimensional Space

To compare image 2130 against image 2100 in n-dimensional space 102,engine 522 compares each sub-string correlithm object 1206 v ₁₁₋₁₉pairwise against each sub-string correlithm object 1206 v ₄₁₋₄₉ todetermine a plurality of anti-Hamming distances and stores them in afirst distance table, as described above with regard to FIGS. 20A-B.Engine 522 determines whether there is any discernible pattern ofsimilarity in the first distance table among any group of neighboringsub-string correlithm objects 1206 v ₁₁₋₁₉ and 1206 v ₄₁₋₄₉, asrepresented by the calculated anti-Hamming distances, as described abovewith regard to FIGS. 20A-B. If such a pattern of similarity is found(e.g., a trace), then engine 522 calculates a vertical compositeanti-Hamming distance 2136 by summing the anti-Hamming distance valueswithin the pattern.

Engine 522 also compares each sub-string correlithm object 1206 h ₁₁₋₁₉pairwise against each sub-string correlithm object 1206 h ₄₁₋₄₉ todetermine a plurality of anti-Hamming distances and stores them in asecond distance table, as described above with regard to FIGS. 20A-B.Engine 522 determines whether there is any discernible pattern ofsimilarity in the second distance table among any group of neighboringsub-string correlithm objects 1206 h ₁₁₋₁₉ and 1206 h ₄₁₋₄₉, asrepresented by the calculated anti-Hamming distances, as described abovewith regard to FIGS. 20A-B. If such a pattern of similarity is found(e.g., a trace), then engine 522 calculates a horizontal compositeanti-Hamming distance 2128 by summing the anti-Hamming distance valueswithin the pattern.

Engine 522 determines a composite anti-Hamming distance 2139 by summingthe vertical composite anti-Hamming distance 2136 and the horizontalcomposite anti-Hamming distance 2138. Engine 522 determines whether theimage 2130 is statistically similar to, or a match of, image 2100 basedon the magnitude of the calculated composite anti-Hamming distance 2139in comparison to a threshold. For example, in one embodiment, acomposite anti-Hamming distance 2139 that is roughly four standarddeviations greater than a standard distance composite value for then-dimensional string correlithm object 602 is considered to bestatistically similar.

Once engine 522 performs the comparisons of images 2110, 2120, and 2130with image 2100 in n-dimensional space 102, as described above, itcompares the composite anti-Hamming distance calculations 2119, 2129,and 2139 to determine which image is the closest match to image 2100. Inparticular, the largest composite anti-Hamming distance among thecalculations 2119, 2129, and 2139 is determined to be the closest matchto image 2100. Using the example images described above with respect toFIGS. 21A-D, the image 2120 of the woman wearing glasses is most likelyto be the closest match to the image 2100 of the woman without theglasses, and therefore it is expected that composite anti-Hammingdistance calculation 2129 would be greater than the anti-Hammingdistance calculation 2119 associated with the image 2110 of the man, andgreater than the anti-Hamming distance calculation 2139 associated withthe image 2130 of the young man. In this way, engine 522 is able toperform a comparison of multi-dimensional data objects in n-dimensionalspace using string correlithm objects 602 h and 602 v instead of themore computationally burdensome approach using dynamic time warpingalgorithms.

While several embodiments have been provided in the present disclosure,it should be understood that the disclosed systems and methods might beembodied in many other specific forms without departing from the spiritor scope of the present disclosure. The present examples are to beconsidered as illustrative and not restrictive, and the intention is notto be limited to the details given herein. For example, the variouselements or components may be combined or integrated in another systemor certain features may be omitted, or not implemented.

In addition, techniques, systems, subsystems, and methods described andillustrated in the various embodiments as discrete or separate may becombined or integrated with other systems, modules, techniques, ormethods without departing from the scope of the present disclosure.Other items shown or discussed as coupled or directly coupled orcommunicating with each other may be indirectly coupled or communicatingthrough some interface, device, or intermediate component whetherelectrically, mechanically, or otherwise. Other examples of changes,substitutions, and alterations are ascertainable by one skilled in theart and could be made without departing from the spirit and scopedisclosed herein.

To aid the Patent Office, and any readers of any patent issued on thisapplication in interpreting the claims appended hereto, applicants notethat they do not intend any of the appended claims to invoke 35 U.S.C. §112(f) as it exists on the date of filing hereof unless the words “meansfor” or “step for” are explicitly used in the particular claim.

1. A correlithm object processing system, comprising: a memoryconfigured to store: a sample two-dimensional data object; a horizontalstring correlithm object associated with the sample two-dimensional dataobject, the horizontal string correlithm object comprising a firstplurality of sub-string correlithm objects; a vertical string correlithmobject associated with the sample two-dimensional data object, thevertical string correlithm object comprising a second plurality ofsub-string correlithm objects; an example two-dimensional data object; ahorizontal string correlithm object associated with the exampletwo-dimensional data object, the horizontal string correlithm objectcomprising a third plurality of sub-string correlithm objects; avertical string correlithm object associated with the exampletwo-dimensional data object, the vertical string correlithm objectcomprising a fourth plurality of sub-string correlithm objects; a stringcorrelithm object engine communicatively coupled to the memory andconfigured to: determine a horizontal composite anti-Hamming distancebased on a comparison of the horizontal string correlithm objectassociated with the sample two-dimensional data object and thehorizontal string correlithm object associated with the exampletwo-dimensional data object; determine a vertical composite anti-Hammingdistance based on a comparison of the vertical string correlithm objectassociated with the sample two-dimensional data object and the verticalstring correlithm object associated with the example two-dimensionaldata object; determine a composite anti-Hamming distance by summing thevertical composite anti-Hamming distance and the horizontal compositeanti-Hamming distance; and determine a quality of a match between theexample two-dimensional data object and the sample two-dimensional dataobject based on the composite anti-Hamming distance.
 2. The correlithmobject processing system of claim 1, wherein the sample two-dimensionaldata object comprises a photograph.
 3. The correlithm object processingsystem of claim 2, wherein determining the horizontal compositeanti-Hamming distance comprises: determining a first plurality ofanti-Hamming distances between a first sub-string correlithm object ofthe horizontal string correlithm object associated with the exampletwo-dimensional data object and each of the sub-string correlithmobjects of the horizontal string correlithm object associated with thesample two-dimensional data object; storing the first plurality ofanti-Hamming distances in a first column of a distance table;determining a second plurality of anti-Hamming distances between asecond sub-string correlithm object of the horizontal string correlithmobject associated with the example two-dimensional data object and eachof the sub-string correlithm objects of the horizontal string correlithmobject associated with the sample two-dimensional data object; storingthe second plurality of anti-Hamming distances in a second column of thedistance table; determining an m-th plurality of anti-Hamming distancesbetween an m-th sub-string correlithm object of the horizontal stringcorrelithm object associated with the example two-dimensional dataobject and each of the sub-string correlithm objects of the horizontalstring correlithm object associated with the sample two-dimensional dataobject; storing the m-th plurality of anti-Hamming distances in an m-thcolumn of the distance table; identifying a group of neighboringanti-Hamming distances stored in the distance table that are greaterthan a predetermined number of standard deviations beyond the standarddistance; and summing the group of neighboring anti-Hamming distancesstored in the distance table as the horizontal composite anti-Hammingdistance.
 4. The correlithm object processing system of claim 2, whereindetermining the vertical composite anti-Hamming distance comprises:determining a first plurality of anti-Hamming distances between a firstsub-string correlithm object of the vertical string correlithm objectassociated with the example two-dimensional data object and each of thesub-string correlithm objects of the vertical string correlithm objectassociated with the sample two-dimensional data object; storing thefirst plurality of anti-Hamming distances in a first column of adistance table; determining a second plurality of anti-Hamming distancesbetween a second sub-string correlithm object of the vertical stringcorrelithm object associated with the example two-dimensional dataobject and each of the sub-string correlithm objects of the verticalstring correlithm object associated with the sample two-dimensional dataobject; storing the second plurality of anti-Hamming distances in asecond column of the distance table; determining an m-th plurality ofanti-Hamming distances between an m-th sub-string correlithm object ofthe vertical string correlithm object associated with the exampletwo-dimensional data object and each of the sub-string correlithmobjects of the vertical string correlithm object associated with thesample two-dimensional data object; storing the m-th plurality ofanti-Hamming distances in an m-th column of the distance table;identifying a group of neighboring anti-Hamming distances stored in thedistance table that are greater than a predetermined number of standarddeviations beyond the standard distance; and summing the group ofneighboring anti-Hamming distances stored in the distance table as thevertical composite anti-Hamming distance.
 5. The correlithm objectprocessing system of claim 1, wherein: the memory is further configuredto store: a second example two-dimensional data object; a horizontalstring correlithm object associated with the second exampletwo-dimensional data object, the horizontal string correlithm objectcomprising a fifth plurality of sub-string correlithm objects; avertical string correlithm object associated with the second exampletwo-dimensional data object, the vertical string correlithm objectcomprising a sixth plurality of sub-string correlithm objects; thestring correlithm object engine is further configured to: determine asecond horizontal composite anti-Hamming distance based on a comparisonof the horizontal string correlithm object associated with the sampletwo-dimensional data object and the horizontal string correlithm objectassociated with the second example two-dimensional data object;determine a second vertical composite anti-Hamming distance based on acomparison of the vertical string correlithm object associated with thesample two-dimensional data object and the vertical string correlithmobject associated with the second example two-dimensional data object;determine a second composite anti-Hamming distance by summing the secondvertical composite anti-Hamming distance and the second horizontalcomposite anti-Hamming distance; and determine a quality of a matchbetween the second example two-dimensional data object and the sampletwo-dimensional data object based on the second composite anti-Hammingdistance.
 6. The correlithm object processing system of claim 5, whereinthe string correlithm object engine is further configured to: determinethat the second composite anti-Hamming distance is greater than thefirst composite anti-Hamming distance; and determine that the secondexample two-dimensional data object is a closer match to the sampletwo-dimensional data object than the first example two-dimensional dataobject based upon determining that the second composite anti-Hammingdistance is greater than the first composite anti-Hamming distance. 7.The correlithm object processing system of claim 1, wherein: the firstplurality of sub-string correlithm objects represent horizontal slicesof real-world data in the sample two-dimensional data object; and thesecond plurality of sub-string correlithm objects represent verticalslices of real-world data in the sample two-dimensional data object. 8.A method for processing string correlithm objects, comprising: storing asample two-dimensional data object; storing a horizontal stringcorrelithm object associated with the sample two-dimensional dataobject, the horizontal string correlithm object comprising a firstplurality of sub-string correlithm objects; storing a vertical stringcorrelithm object associated with the sample two-dimensional dataobject, the vertical string correlithm object comprising a secondplurality of sub-string correlithm objects; storing an exampletwo-dimensional data object; storing a horizontal string correlithmobject associated with the example two-dimensional data object, thehorizontal string correlithm object comprising a third plurality ofsub-string correlithm objects; storing a vertical string correlithmobject associated with the example two-dimensional data object, thevertical string correlithm object comprising a fourth plurality ofsub-string correlithm objects; determining a horizontal compositeanti-Hamming distance based on a comparison of the horizontal stringcorrelithm object associated with the sample two-dimensional data objectand the horizontal string correlithm object associated with the exampletwo-dimensional data object; determining a vertical compositeanti-Hamming distance based on a comparison of the vertical stringcorrelithm object associated with the sample two-dimensional data objectand the vertical string correlithm object associated with the exampletwo-dimensional data object; determining a composite anti-Hammingdistance by summing the vertical composite anti-Hamming distance and thehorizontal composite anti-Hamming distance; and determining a quality ofa match between the example two-dimensional data object and the sampletwo-dimensional data object based on the composite anti-Hammingdistance.
 9. The method of claim 8, wherein the sample two-dimensionaldata object comprises a photograph.
 10. The method of claim 9, whereindetermining the horizontal composite anti-Hamming distance comprises:determining a first plurality of anti-Hamming distances between a firstsub-string correlithm object of the horizontal string correlithm objectassociated with the example two-dimensional data object and each of thesub-string correlithm objects of the horizontal string correlithm objectassociated with the sample two-dimensional data object; storing thefirst plurality of anti-Hamming distances in a first column of adistance table; determining a second plurality of anti-Hamming distancesbetween a second sub-string correlithm object of the horizontal stringcorrelithm object associated with the example two-dimensional dataobject and each of the sub-string correlithm objects of the horizontalstring correlithm object associated with the sample two-dimensional dataobject; storing the second plurality of anti-Hamming distances in asecond column of the distance table; determining an m-th plurality ofanti-Hamming distances between an m-th sub-string correlithm object ofthe horizontal string correlithm object associated with the exampletwo-dimensional data object and each of the sub-string correlithmobjects of the horizontal string correlithm object associated with thesample two-dimensional data object; storing the m-th plurality ofanti-Hamming distances in an m-th column of the distance table;identifying a group of neighboring anti-Hamming distances stored in thedistance table that are greater than a predetermined number of standarddeviations beyond the standard distance; and summing the group ofneighboring anti-Hamming distances stored in the distance table as thehorizontal composite anti-Hamming distance.
 11. The method of claim 9,wherein determining the vertical composite anti-Hamming distancecomprises: determining a first plurality of anti-Hamming distancesbetween a first sub-string correlithm object of the vertical stringcorrelithm object associated with the example two-dimensional dataobject and each of the sub-string correlithm objects of the verticalstring correlithm object associated with the sample two-dimensional dataobject; storing the first plurality of anti-Hamming distances in a firstcolumn of a distance table; determining a second plurality ofanti-Hamming distances between a second sub-string correlithm object ofthe vertical string correlithm object associated with the exampletwo-dimensional data object and each of the sub-string correlithmobjects of the vertical string correlithm object associated with thesample two-dimensional data object; storing the second plurality ofanti-Hamming distances in a second column of the distance table;determining an m-th plurality of anti-Hamming distances between an m-thsub-string correlithm object of the vertical string correlithm objectassociated with the example two-dimensional data object and each of thesub-string correlithm objects of the vertical string correlithm objectassociated with the sample two-dimensional data object; storing the m-thplurality of anti-Hamming distances in an m-th column of the distancetable; identifying a group of neighboring anti-Hamming distances storedin the distance table that are greater than a predetermined number ofstandard deviations beyond the standard distance; and summing the groupof neighboring anti-Hamming distances stored in the distance table asthe vertical composite anti-Hamming distance.
 12. The method of claim 8,further comprising: storing a second example two-dimensional dataobject; storing a horizontal string correlithm object associated withthe second example two-dimensional data object, the horizontal stringcorrelithm object comprising a fifth plurality of sub-string correlithmobjects; storing a vertical string correlithm object associated with thesecond example two-dimensional data object, the vertical stringcorrelithm object comprising a sixth plurality of sub-string correlithmobjects; determining a second horizontal composite anti-Hamming distancebased on a comparison of the horizontal string correlithm objectassociated with the sample two-dimensional data object and thehorizontal string correlithm object associated with the second exampletwo-dimensional data object; determining a second vertical compositeanti-Hamming distance based on a comparison of the vertical stringcorrelithm object associated with the sample two-dimensional data objectand the vertical string correlithm object associated with the secondexample two-dimensional data object; determining a second compositeanti-Hamming distance by summing the second vertical compositeanti-Hamming distance and the second horizontal composite anti-Hammingdistance; and determining a quality of a match between the secondexample two-dimensional data object and the sample two-dimensional dataobject based on the second composite anti-Hamming distance.
 13. Themethod of claim 12, further comprising: determining that the secondcomposite anti-Hamming distance is greater than the first compositeanti-Hamming distance; and determining that the second exampletwo-dimensional data object is a closer match to the sampletwo-dimensional data object than the first example two-dimensional dataobject based upon determining that the second composite anti-Hammingdistance is greater than the first composite anti-Hamming distance. 14.The method of claim 8, wherein: the first plurality of sub-stringcorrelithm objects represent horizontal slices of real-world data in thesample two-dimensional data object; and the second plurality ofsub-string correlithm objects represent vertical slices of real-worlddata in the sample two-dimensional data object.
 15. A computer programcomprising executable instructions stored in a non-transitory computerreadable medium such that when executed by a processor causes theprocessor to emulate a correlithm object processing system configuredto: store a sample two-dimensional data object; store a horizontalstring correlithm object associated with the sample two-dimensional dataobject, the horizontal string correlithm object comprising a firstplurality of sub-string correlithm objects; store a vertical stringcorrelithm object associated with the sample two-dimensional dataobject, the vertical string correlithm object comprising a secondplurality of sub-string correlithm objects; store an exampletwo-dimensional data object; store a horizontal string correlithm objectassociated with the example two-dimensional data object, the horizontalstring correlithm object comprising a third plurality of sub-stringcorrelithm objects; store a vertical string correlithm object associatedwith the example two-dimensional data object, the vertical stringcorrelithm object comprising a fourth plurality of sub-string correlithmobjects; determine a horizontal composite anti-Hamming distance based ona comparison of the horizontal string correlithm object associated withthe sample two-dimensional data object and the horizontal stringcorrelithm object associated with the example two-dimensional dataobject; determine a vertical composite anti-Hamming distance based on acomparison of the vertical string correlithm object associated with thesample two-dimensional data object and the vertical string correlithmobject associated with the example two-dimensional data object;determine a composite anti-Hamming distance by summing the verticalcomposite anti-Hamming distance and the horizontal compositeanti-Hamming distance; and determine a quality of a match between theexample two-dimensional data object and the sample two-dimensional dataobject based on the composite anti-Hamming distance.
 16. The computerprogram of claim 15, wherein the sample two-dimensional data objectcomprises a photograph.
 17. The computer program of claim 16, whereindetermining the horizontal composite anti-Hamming distance comprises:determining a first plurality of anti-Hamming distances between a firstsub-string correlithm object of the horizontal string correlithm objectassociated with the example two-dimensional data object and each of thesub-string correlithm objects of the horizontal string correlithm objectassociated with the sample two-dimensional data object; storing thefirst plurality of anti-Hamming distances in a first column of adistance table; determining a second plurality of anti-Hamming distancesbetween a second sub-string correlithm object of the horizontal stringcorrelithm object associated with the example two-dimensional dataobject and each of the sub-string correlithm objects of the horizontalstring correlithm object associated with the sample two-dimensional dataobject; storing the second plurality of anti-Hamming distances in asecond column of the distance table; determining an m-th plurality ofanti-Hamming distances between an m-th sub-string correlithm object ofthe horizontal string correlithm object associated with the exampletwo-dimensional data object and each of the sub-string correlithmobjects of the horizontal string correlithm object associated with thesample two-dimensional data object; storing the m-th plurality ofanti-Hamming distances in an m-th column of the distance table;identifying a group of neighboring anti-Hamming distances stored in thedistance table that are greater than a predetermined number of standarddeviations beyond the standard distance; and summing the group ofneighboring anti-Hamming distances stored in the distance table as thehorizontal composite anti-Hamming distance.
 18. The computer program ofclaim 16, wherein determining the vertical composite anti-Hammingdistance comprises: determining a first plurality of anti-Hammingdistances between a first sub-string correlithm object of the verticalstring correlithm object associated with the example two-dimensionaldata object and each of the sub-string correlithm objects of thevertical string correlithm object associated with the sampletwo-dimensional data object; storing the first plurality of anti-Hammingdistances in a first column of a distance table; determining a secondplurality of anti-Hamming distances between a second sub-stringcorrelithm object of the vertical string correlithm object associatedwith the example two-dimensional data object and each of the sub-stringcorrelithm objects of the vertical string correlithm object associatedwith the sample two-dimensional data object; storing the secondplurality of anti-Hamming distances in a second column of the distancetable; determining an m-th plurality of anti-Hamming distances betweenan m-th sub-string correlithm object of the vertical string correlithmobject associated with the example two-dimensional data object and eachof the sub-string correlithm objects of the vertical string correlithmobject associated with the sample two-dimensional data object; storingthe m-th plurality of anti-Hamming distances in an m-th column of thedistance table; identifying a group of neighboring anti-Hammingdistances stored in the distance table that are greater than apredetermined number of standard deviations beyond the standarddistance; and summing the group of neighboring anti-Hamming distancesstored in the distance table as the vertical composite anti-Hammingdistance.
 19. The computer program of claim 15, further configured to:store a second example two-dimensional data object; store a horizontalstring correlithm object associated with the second exampletwo-dimensional data object, the horizontal string correlithm objectcomprising a fifth plurality of sub-string correlithm objects; store avertical string correlithm object associated with the second exampletwo-dimensional data object, the vertical string correlithm objectcomprising a sixth plurality of sub-string correlithm objects; determinea second horizontal composite anti-Hamming distance based on acomparison of the horizontal string correlithm object associated withthe sample two-dimensional data object and the horizontal stringcorrelithm object associated with the second example two-dimensionaldata object; determine a second vertical composite anti-Hamming distancebased on a comparison of the vertical string correlithm objectassociated with the sample two-dimensional data object and the verticalstring correlithm object associated with the second exampletwo-dimensional data object; determine a second composite anti-Hammingdistance by summing the second vertical composite anti-Hamming distanceand the second horizontal composite anti-Hamming distance; and determinea quality of a match between the second example two-dimensional dataobject and the sample two-dimensional data object based on the secondcomposite anti-Hamming distance.
 20. The computer program of claim 19,further configured to: determine that the second composite anti-Hammingdistance is greater than the first composite anti-Hamming distance; anddetermine that the second example two-dimensional data object is acloser match to the sample two-dimensional data object than the firstexample two-dimensional data object based upon determining that thesecond composite anti-Hamming distance is greater than the firstcomposite anti-Hamming distance.